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Developmental Mathematics

Elayn Martin-Gay

Chapter 13

Factoring Polynomials - all with Video Answers

Educators

Section 1

The Greatest Common Factor and Factoring by Grouping

01:25

Problem 1

Find the GCF for each list. See Examples I through 3.
32,36

Danielle Leedy
Danielle Leedy
Numerade Educator
01:14

Problem 2

Find the GCF for each list. See Examples I through 3.
36,90

Danielle Leedy
Danielle Leedy
Numerade Educator
01:14

Problem 3

Find the GCF for each list. See Examples I through 3.
$18,42,84$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:37

Problem 4

Find the GCF for each list. See Examples I through 3.
$30,75,135$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:14

Problem 5

Find the GCF for each list. See Examples I through 3.
$24,14,21$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:10

Problem 6

Find the GCF for each list. See Examples I through 3.
$15,25,27$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:44

Problem 7

Find the GCF for each list. See Examples I through 3.
$y^2, y^4, y^7$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:46

Problem 8

Find the GCF for each list. See Examples I through 3.
$x^3, x^2, x^5$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:25

Problem 9

Find the GCF for each list. See Examples I through 3.
$z^7, z^9, z^{11}$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:53

Problem 10

Find the GCF for each list. See Examples I through 3.
$y^8, y^{10}, y^{12}$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:20

Problem 11

Find the GCF for each list. See Examples I through 3.
$x^{10} y^2, x y^2, x^3 y^3$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:12

Problem 12

Find the GCF for each list. See Examples I through 3.
$p^7 q, p^8 q^2, p^9 q^3$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:25

Problem 13

Find the GCF for each list. See Examples I through 3.
$14 x, 21$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:05

Problem 14

Find the GCF for each list. See Examples I through 3.
$20 y, 15$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:45

Problem 15

Find the GCF for each list. See Examples I through 3.
$12 y^4, 20 y^3$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:49

Problem 16

Find the GCF for each list. See Examples I through 3.
$32 x^5, 18 x^2$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:35

Problem 17

Find the GCF for each list. See Examples I through 3.
$-10 x^2, 15 x^3$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:39

Problem 18

Find the GCF for each list. See Examples I through 3.
$-21 x^3, 14 x$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:58

Problem 19

Find the GCF for each list. See Examples I through 3.
$12 x^3,-6 x^4, 3 x^5$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:05

Problem 20

Find the GCF for each list. See Examples I through 3.
$15 y^2, 5 y^7,-20 y^3$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:32

Problem 21

Find the GCF for each list. See Examples I through 3.
$-18 x^2 y, 9 x^3 y^3, 36 x^3 y$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:15

Problem 22

Find the GCF for each list. See Examples I through 3.
$7 x^3 y^3,-21 x^2 y^2, 14 x y^4$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:41

Problem 23

Find the GCF for each list. See Examples I through 3.
$20 a^6 b^2 c^8, 50 a^7 b$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:58

Problem 24

Find the GCF for each list. See Examples I through 3.
$40 x^7 y^2 z, 64 x^9 y$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:14

Problem 25

Factor out the GCF from each polynomial. See Examples 4 through 10.
$3 a+6$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:33

Problem 26

Factor out the GCF from each polynomial. See Examples 4 through 10.
$18 a+12$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
02:06

Problem 27

Factor out the GCF from each polynomial. See Examples 4 through 10.
$30 x-15$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:05

Problem 28

Factor out the GCF from each polynomial. See Examples 4 through 10.
$42 x-7$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:51

Problem 29

Factor out the GCF from each polynomial. See Examples 4 through 10.
$x^3+5 x^2$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:03

Problem 30

Factor out the GCF from each polynomial. See Examples 4 through 10.
$y^5+6 y^4$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:21

Problem 31

Factor out the GCF from each polynomial. See Examples 4 through 10.
$6 y^4+2 y^3$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:33

Problem 32

Factor out the GCF from each polynomial. See Examples 4 through 10.
$5 x^2+10 x^6$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:29

Problem 33

Factor out the GCF from each polynomial. See Examples 4 through 10.
$32 x y-18 x^2$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:42

Problem 34

Factor out the GCF from each polynomial. See Examples 4 through 10.
$10 x y-15 x^2$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:07

Problem 35

Factor out the GCF from each polynomial. See Examples 4 through 10.
$4 x-8 y+4$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:11

Problem 36

Factor out the GCF from each polynomial. See Examples 4 through 10.
$7 x+21 y-7$

Danielle Leedy
Danielle Leedy
Numerade Educator
02:06

Problem 37

Factor out the GCF from each polynomial. See Examples 4 through 10.
$6 x^3-9 x^2+12 x$

Danielle Leedy
Danielle Leedy
Numerade Educator
02:21

Problem 38

Factor out the GCF from each polynomial. See Examples 4 through 10.
$12 x^3+16 x^2-8 x$

Danielle Leedy
Danielle Leedy
Numerade Educator
02:49

Problem 39

Factor out the GCF from each polynomial. See Examples 4 through 10.
$a^7 b^6-a^3 b^2+a^2 b^5-a^2 b^2$

Danielle Leedy
Danielle Leedy
Numerade Educator
02:28

Problem 40

Factor out the GCF from each polynomial. See Examples 4 through 10.
$x^9 y^6+x^3 y^5-x^4 y^3+x^3 y^3$

Danielle Leedy
Danielle Leedy
Numerade Educator
02:04

Problem 41

Factor out the GCF from each polynomial. See Examples 4 through 10.
$5 x^3 y-15 x^2 y+10 x y$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:47

Problem 42

Factor out the GCF from each polynomial. See Examples 4 through 10.
$14 x^3 y+7 x^2 y-7 x y$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
02:12

Problem 43

Factor out the GCF from each polynomial. See Examples 4 through 10.
$8 x^5+16 x^4-20 x^3+12$

Danielle Leedy
Danielle Leedy
Numerade Educator
02:07

Problem 44

Factor out the GCF from each polynomial. See Examples 4 through 10.
$9 y^6-27 y^4+18 y^2+6$

Danielle Leedy
Danielle Leedy
Numerade Educator
03:36

Problem 45

Factor out the GCF from each polynomial. See Examples 4 through 10.
$\frac{1}{3} x^4+\frac{2}{3} x^3-\frac{4}{3} x^5+\frac{1}{3} x$

Danielle Leedy
Danielle Leedy
Numerade Educator
02:58

Problem 46

Factor out the GCF from each polynomial. See Examples 4 through 10.
$\frac{2}{5} y^7-\frac{4}{5} y^5+\frac{3}{5} y^2-\frac{2}{5} y$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:38

Problem 47

Factor out the GCF from each polynomial. See Examples 4 through 10.
$y\left(x^2+2\right)+3\left(x^2+2\right)$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:06

Problem 48

Factor out the GCF from each polynomial. See Examples 4 through 10.
$x\left(y^2+1\right)-3\left(y^2+1\right)$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:35

Problem 49

Factor out the GCF from each polynomial. See Examples 4 through 10.
$z(y+4)+3(y+4)$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:39

Problem 50

Factor out the GCF from each polynomial. See Examples 4 through 10.
$8(x+2)-y(x+2)$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:46

Problem 51

Factor out the GCF from each polynomial. See Examples 4 through 10.
$r\left(z^2-6\right)+\left(z^2-6\right)$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:46

Problem 52

Factor out the GCF from each polynomial. See Examples 4 through 10.
$q\left(b^3-5\right)+\left(b^3-5\right)$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:40

Problem 53

Factor a negative number or a GCF with a negative coefficient from each polynomial. See Example 5.
$-2 x-14$

Danielle Leedy
Danielle Leedy
Numerade Educator
00:35

Problem 54

Factor a negative number or a GCF with a negative coefficient from each polynomial. See Example 5.
$-7 y-21$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:16

Problem 55

Factor a negative number or a GCF with a negative coefficient from each polynomial. See Example 5.
$-2 x^5+x^7$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:29

Problem 56

Factor a negative number or a GCF with a negative coefficient from each polynomial. See Example 5.
$-5 y^3+y^6$

Danielle Leedy
Danielle Leedy
Numerade Educator
02:00

Problem 57

Factor a negative number or a GCF with a negative coefficient from each polynomial. See Example 5.
$-6 a^4+9 a^3-3 a^2$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:34

Problem 58

Factor a negative number or a GCF with a negative coefficient from each polynomial. See Example 5.
$-5 m^6+10 m^5-5 m^3$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:31

Problem 59

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$x^3+2 x^2+5 x+10$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:28

Problem 60

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$x^3+4 x^2+3 x+12$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:12

Problem 61

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$5 x+15+x y+3 y$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:00

Problem 62

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$x y+y+2 x+2$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:32

Problem 63

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$6 x^3-4 x^2+15 x-10$

Danielle Leedy
Danielle Leedy
Numerade Educator
01:35

Problem 64

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$16 x^3-28 x^2+12 x-21$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
02:05

Problem 65

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$5 m^3+6 m n+5 m^2+6 n$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:59

Problem 66

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$8 w^2+7 w v+8 w+7 v$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:13

Problem 67

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$2 y-8+x y-4 x$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:08

Problem 68

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$6 x-42+x y-7 y$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:58

Problem 69

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$2 x^3+x^2+8 x+4$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:07

Problem 70

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$2 x^3-x^2-10 x+5$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:20

Problem 71

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$3 x-3+x^3-4 x^2$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:09

Problem 72

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$7 x-21+x^3-2 x^2$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:23

Problem 73

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$4 x^2-8 x y-3 x+6 y$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:15

Problem 74

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$5 x y-15 x-6 y+18$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:15

Problem 75

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$5 q^2-4 p q-5 q+4 p$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:08

Problem 76

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." See Examples 11 through 17 .
$6 m^2-5 m n-6 m+5 n$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:59

Problem 77

Factor out the GCF from each polynomial Then factor by grouping.
$12 x^2 y-42 x^2-4 y+14$

Erika Bustos
Erika Bustos
Numerade Educator
01:07

Problem 78

Factor out the GCF from each polynomial Then factor by grouping.
$90+15 y^2-18 x-3 x y^2$

Erika Bustos
Erika Bustos
Numerade Educator
00:52

Problem 79

Factor out the GCF from each polynomial Then factor by grouping.
$6 a^2+9 a b^2+6 a b+9 b^3$

Erika Bustos
Erika Bustos
Numerade Educator
00:56

Problem 80

Factor out the GCF from each polynomial Then factor by grouping.
$16 x^2+4 x y^2+8 x y+2 y^3$

Erika Bustos
Erika Bustos
Numerade Educator
01:10

Problem 81

Multiply. See Section 12.5.
$(x+2)(x+5)$

Deboney Harris
Deboney Harris
Numerade Educator
01:06

Problem 82

Multiply. See Section 12.5.
$(y+3)(y+6)$

Deboney Harris
Deboney Harris
Numerade Educator
01:04

Problem 83

Multiply. See Section 12.5.
$(b+1)(b-4)$

Deboney Harris
Deboney Harris
Numerade Educator
01:17

Problem 84

Multiply. See Section 12.5.
$(x-5)(x+10)$

Deboney Harris
Deboney Harris
Numerade Educator
00:42

Problem 85

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|r|r|r|r|r|c|}
\hline & & . & . & . & . & . & . & . & . \\
\hline \text { Two Numbers } & 4,7 & & & & & & & & \\
\hline \text { Their Product } & 28 & 12 & 20 & 8 & 16 & -10 & -9 & -24 & -36 \\
\hline \text { Their Sum } & 11 & 8 & 9 & -9 & -10 & 3 & 0 & -5 & -5 \\
\hline
\end{array}
$$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:42

Problem 86

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|r|r|r|r|r|c|}
\hline & & . & . & . & . & . & . & . & . \\
\hline \text { Two Numbers } & 4,7 & & & & & & & & \\
\hline \text { Their Product } & 28 & 12 & 20 & 8 & 16 & -10 & -9 & -24 & -36 \\
\hline \text { Their Sum } & 11 & 8 & 9 & -9 & -10 & 3 & 0 & -5 & -5 \\
\hline
\end{array}
$$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:42

Problem 87

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|r|r|r|r|r|c|}
\hline & & . & . & . & . & . & . & . & . \\
\hline \text { Two Numbers } & 4,7 & & & & & & & & \\
\hline \text { Their Product } & 28 & 12 & 20 & 8 & 16 & -10 & -9 & -24 & -36 \\
\hline \text { Their Sum } & 11 & 8 & 9 & -9 & -10 & 3 & 0 & -5 & -5 \\
\hline
\end{array}
$$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:42

Problem 88

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|r|r|r|r|r|c|}
\hline & & . & . & . & . & . & . & . & . \\
\hline \text { Two Numbers } & 4,7 & & & & & & & & \\
\hline \text { Their Product } & 28 & 12 & 20 & 8 & 16 & -10 & -9 & -24 & -36 \\
\hline \text { Their Sum } & 11 & 8 & 9 & -9 & -10 & 3 & 0 & -5 & -5 \\
\hline
\end{array}
$$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:42

Problem 89

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|r|r|r|r|r|c|}
\hline & & . & . & . & . & . & . & . & . \\
\hline \text { Two Numbers } & 4,7 & & & & & & & & \\
\hline \text { Their Product } & 28 & 12 & 20 & 8 & 16 & -10 & -9 & -24 & -36 \\
\hline \text { Their Sum } & 11 & 8 & 9 & -9 & -10 & 3 & 0 & -5 & -5 \\
\hline
\end{array}
$$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:42

Problem 90

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|r|r|r|r|r|c|}
\hline & & . & . & . & . & . & . & . & . \\
\hline \text { Two Numbers } & 4,7 & & & & & & & & \\
\hline \text { Their Product } & 28 & 12 & 20 & 8 & 16 & -10 & -9 & -24 & -36 \\
\hline \text { Their Sum } & 11 & 8 & 9 & -9 & -10 & 3 & 0 & -5 & -5 \\
\hline
\end{array}
$$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:42

Problem 91

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|r|r|r|r|r|c|}
\hline & & . & . & . & . & . & . & . & . \\
\hline \text { Two Numbers } & 4,7 & & & & & & & & \\
\hline \text { Their Product } & 28 & 12 & 20 & 8 & 16 & -10 & -9 & -24 & -36 \\
\hline \text { Their Sum } & 11 & 8 & 9 & -9 & -10 & 3 & 0 & -5 & -5 \\
\hline
\end{array}
$$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:42

Problem 92

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|r|r|r|r|r|c|}
\hline & & . & . & . & . & . & . & . & . \\
\hline \text { Two Numbers } & 4,7 & & & & & & & & \\
\hline \text { Their Product } & 28 & 12 & 20 & 8 & 16 & -10 & -9 & -24 & -36 \\
\hline \text { Their Sum } & 11 & 8 & 9 & -9 & -10 & 3 & 0 & -5 & -5 \\
\hline
\end{array}
$$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:44

Problem 93

See the Concept Checks in this section.
Which of the following is/are factored form(s) of $-2 x+14$ ?
a. $-2(x+7)$
b. $-2 \cdot x+14$
c. $-2(x-14)$
d. $-2(x-7)$

Chelsea Hoke
Chelsea Hoke
Numerade Educator
00:28

Problem 94

See the Concept Checks in this section.
Which of the following is/are factored form(s) of $8 a-24$ ?
a. $8 \cdot a-24$
b. $8(a-3)$
c. $4(2 a-12)$
d. $8 \cdot a-2 \cdot 12$

Deboney Harris
Deboney Harris
Numerade Educator
00:54

Problem 95

Which of the following expressions are factored?
$(a+6)(a+2)$

Deboney Harris
Deboney Harris
Numerade Educator
00:49

Problem 96

Which of the following expressions are factored?
$(x+5)(x+y)$

Sherrie Fenner
Sherrie Fenner
Numerade Educator
01:05

Problem 97

Which of the following expressions are factored?
$5(2 y+z)-b(2 y+z)$

Deboney Harris
Deboney Harris
Numerade Educator
00:54

Problem 98

Which of the following expressions are factored?
$3 x(a+2 b)+2(a+2 b)$

Deboney Harris
Deboney Harris
Numerade Educator
03:36

Problem 99

The number (in thousands) of students who graduated from U.S. high schools, both public and private, each year during 2000 through 2013 can be modeled by $-3 x^2+78 x+2904$, where $x$ is the number of years since 2000. (Source: National Center for Educational Statistics)
a. Find the number of students who graduated from U.S. high schools in 2010. To do so, let $x=10$ and evaluate $-3 x^2+78 x+2904$.
b. Use this expression to predict the number of students who will graduate from U.S. high schools in 2018.
c. Factor the polynomial $-3 x^2+78 x+2904$ by factoring -3 from each term.
d. For the year 2010, the National Center for Higher Education determined that $62.5 \%$ of U.S. high school graduates went on to higher education. Using your answer from part a, determine how many of those graduating in 2010 pursued higher education.

Deboney Harris
Deboney Harris
Numerade Educator
02:08

Problem 100

The amount of bottled water consumed in the United States, in gallons per person, for the period 2010-2015 can be approximated by the polynomial $-\frac{9}{100} x^2+\frac{246}{100} x+\frac{2594}{100}$, where $x$ is the number of years after 2010. (Source:Bottledwater.org and Fortune)
a. Find the approximate U.S. annual per capita consumption of bottled water in 2014. To do so, let $x=4$ and evaluate $-\frac{9}{100} x^2+\frac{246}{100} x+\frac{2594}{100}$
b. Find the approximate U.S. annual per capita consumption of bottled water in 2015.
c. Suppose the annual per capita consumption of bottled water continues to be approximated by the polynomial $-\frac{9}{100} x^2+\frac{246}{100} x+\frac{2594}{100}$. Use this polynomial to predict the per capita consumption of bottled water in 2020.
d. Factor out the GCF $\frac{1}{100}$ from the polynomial $-\frac{9}{100} x^2+\frac{246}{100} x+\frac{2594}{100}$

Jon Southam
Jon Southam
Numerade Educator
03:14

Problem 101

The annual orange production (in thousand tons) in the United States for the period 20112016 can be approximated by the polynomial $87 x^2-1131 x+9048$, where $x$ is the number of years after 2011. (Source: Based on data from the National Agricultural Statistics Service and bloomberg.com)
a. Find the approximate U.S. orange production in 2015. To do so, let $x=4$ and evaluate $87 x^2-1131 x+9048$
b. Find the approximate U.S. orange production in 2013.
c. Factor out the GCF from the polynomial $87 x^2-1131 x+9048$
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AA
Amy Alred
Numerade Educator
01:04

Problem 102

The polynomial $-6 x^2+72 x+384$ represents the approximate number of visitors (in thousands) per year to Redwoods National Park in California, during 2013-2016. In this polynomial, $x$ represents the years since 2013. (Source: Based on data from the National Park Service)
a. Find the approximate number of visitors to Redwoods National Park in 2014. To do so, let $x=1$ and evaluate $-6 x^2+72 x+384$.
b. Find the approximate number of visitors to Redwoods National Park in 2016.
c. Factor out a common factor of -6 from the polynomial $-6 x^2+72 x+384$
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Erika Bustos
Erika Bustos
Numerade Educator
01:51

Problem 103

Write an expression for the area of each shaded region. Then write the expression as a factored polynomial.
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Deboney Harris
Deboney Harris
Numerade Educator
01:51

Problem 104

Write an expression for the area of each shaded region. Then write the expression as a factored polynomial.
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Deboney Harris
Deboney Harris
Numerade Educator
00:40

Problem 105

Write an expression for the length of each rectangle.
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Ramzi Deek
Ramzi Deek
Numerade Educator
00:40

Problem 106

Write an expression for the length of each rectangle.
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Ramzi Deek
Ramzi Deek
Numerade Educator
01:13

Problem 107

Construct a binomial whose greatest common factor is $5 a^3$.

Deboney Harris
Deboney Harris
Numerade Educator
01:26

Problem 108

Construct a trinomial whose greatest common factor is $2 x^2$. See the hint for Exercise 107.

Chelsea Hoke
Chelsea Hoke
Numerade Educator
01:49

Problem 109

Explain how you can tell whether a polynomial is written in factored form.

Deboney Harris
Deboney Harris
Numerade Educator
01:34

Problem 110

Construct a four-term polynomial that can be factored by grouping Explain how you constructed the polynomial.

Chelsea Hoke
Chelsea Hoke
Numerade Educator