Beginning and Intermediate Algebra

Problem 8

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

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

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

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

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

Numerade Educator

00:25

Problem 13

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

Danielle Leedy

Numerade Educator

00:28

Problem 14

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

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

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

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

Numerade Educator

00:39

Problem 18

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

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

Numerade Educator

Problem 20

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

Danielle Leedy

Numerade Educator

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

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

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

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

Numerade Educator

00:44

Problem 25

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

Danielle Leedy

Numerade Educator

Problem 26

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

Danielle Leedy

Numerade Educator

01:19

Problem 27

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

Danielle Leedy

Numerade Educator

Problem 28

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

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

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

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

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

Numerade Educator

01:07

Problem 33

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

Danielle Leedy

Numerade Educator

01:11

Problem 34

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

Danielle Leedy

Numerade Educator

02:06

Problem 35

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

Danielle Leedy

Numerade Educator

02:21

Problem 36

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

Danielle Leedy

Numerade Educator

02:49

Problem 37

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

Numerade Educator

02:28

Problem 38

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

Numerade Educator

02:12

Problem 39

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

Danielle Leedy

Numerade Educator

02:07

Problem 40

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

Danielle Leedy

Numerade Educator

03:36

Problem 41

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

Numerade Educator

02:58

Problem 42

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

Numerade Educator

00:38

Problem 43

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

Numerade Educator

01:06

Problem 44

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

Numerade Educator

00:35

Problem 45

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

Danielle Leedy

Numerade Educator

00:39

Problem 46

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

Danielle Leedy

Numerade Educator

Problem 47

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

Numerade Educator

Problem 48

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

Numerade Educator

00:40

Problem 49

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

Danielle Leedy

Numerade Educator

00:35

Problem 50

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

Danielle Leedy

Numerade Educator

01:16

Problem 51

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

Danielle Leedy

Numerade Educator

01:29

Problem 52

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

Danielle Leedy

Numerade Educator

02:00

Problem 53

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

Numerade Educator

01:34

Problem 54

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

Numerade Educator

01:42

Problem 55

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
x^{3}+2 x^{2}+5 x+10
$$

Danielle Leedy

Numerade Educator

01:13

Problem 56

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
x^{3}+4 x^{2}+3 x+12
$$

Danielle Leedy

Numerade Educator

01:04

Problem 57

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
5 x+15+x y+3 y
$$

Danielle Leedy

Numerade Educator

01:07

Problem 58

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
x y+y+2 x+2
$$

Danielle Leedy

Numerade Educator

Problem 59

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
6 x^{3}-4 x^{2}+15 x-10
$$

Danielle Leedy

Numerade Educator

Problem 60

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
16 x^{3}-28 x^{2}+12 x-21
$$

Danielle Leedy

Numerade Educator

01:38

Problem 61

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
5 m^{3}+6 m n+5 m^{2}+6 n
$$

Danielle Leedy

Numerade Educator

01:50

Problem 62

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
8 w^{2}+7 w v+8 w+7 v
$$

Danielle Leedy

Numerade Educator

01:15

Problem 63

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
2 y-8+x y-4 x
$$

Danielle Leedy

Numerade Educator

00:59

Problem 64

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
6 x-42+x y-7 y
$$

Danielle Leedy

Numerade Educator

01:10

Problem 65

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
2 x^{3}-x^{2}+8 x-4
$$

Danielle Leedy

Numerade Educator

01:39

Problem 66

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
2 x^{3}-x^{2}-10 x+5
$$

Danielle Leedy

Numerade Educator

01:47

Problem 67

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
4 x^{2}-8 x y-3 x+6 y
$$

Danielle Leedy

Numerade Educator

01:07

Problem 68

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
5 x y-15 x-6 y+18
$$

Danielle Leedy

Numerade Educator

01:39

Problem 69

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
5 q^{2}-4 p q-5 q+4 p
$$

Danielle Leedy

Numerade Educator

01:43

Problem 70

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
6 m^{2}-5 m n-6 m+5 n
$$

Deboney Harris

Numerade Educator

02:33

Problem 71

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
2 x^{4}+5 x^{3}+2 x^{2}+5 x
$$

Danielle Leedy

Numerade Educator

02:12

Problem 72

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
4 y^{4}+y^{2}+20 y^{3}+5 y
$$

Deboney Harris

Numerade Educator

01:57

Problem 73

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
12 x^{2} y-42 x^{2}-4 y+14
$$

Deboney Harris

Numerade Educator

01:53

Problem 74

Factor each four-term polynomial by grouping. See Examples 11 through 16.
$$
90+15 y^{2}-18 x-3 x y^{2}
$$

Deboney Harris

Numerade Educator

01:37

Problem 75

Factor. See Examples 4 through 16.
$$
32 x y-18 x^{2}
$$

Deboney Harris

Numerade Educator

00:53

Problem 76

Factor. See Examples 4 through 16.
$$
10 x y-15 x^{2}
$$

Deboney Harris

Numerade Educator

00:37

Problem 77

Factor. See Examples 4 through 16.
$$
y(x+2)-3(x+2)
$$

Deboney Harris

Numerade Educator

00:33

Problem 78

Factor. See Examples 4 through 16.
$$
z(y-4)+3(y-4)
$$

Deboney Harris

Numerade Educator

03:18

Problem 79

Factor. See Examples 4 through 16.
$$
14 x^{3} y+7 x^{2} y-7 x y
$$

Deboney Harris

Numerade Educator

01:53

Problem 80

Factor. See Examples 4 through 16.
$$
5 x^{3} y-15 x^{2} y+10 x y
$$

Deboney Harris

Numerade Educator

Problem 81

Factor. See Examples 4 through 16.
$$
28 x^{3}-7 x^{2}+12 x-3
$$

Deboney Harris

Numerade Educator

01:26

Problem 82

Factor. See Examples 4 through 16.
$$
15 x^{3}+5 x^{2}-6 x-2
$$

Deboney Harris

Numerade Educator

02:00

Problem 83

Factor. See Examples 4 through 16.
$$
-40 x^{8} y^{6}-16 x^{9} y^{5}
$$

Deboney Harris

Numerade Educator

00:59

Problem 84

Factor. See Examples 4 through 16.
$$
-21 x^{3} y-49 x^{2} y^{2}
$$

Deboney Harris

Numerade Educator

01:54

Problem 85

Factor. See Examples 4 through 16.
$$
6 a^{2}+9 a b^{2}+6 a b+9 b^{3}
$$

Deboney Harris

Numerade Educator

02:08

Problem 86

Factor. See Examples 4 through 16.
$$
16 x^{2}+4 x y^{2}+8 x y+2 y^{3}
$$

Deboney Harris

Numerade Educator

01:10

Problem 87

Multiply. See Section 5.3.
$$
(x+2)(x+5)
$$

Deboney Harris

Numerade Educator

01:06

Problem 88

Multiply. See Section 5.3.
$$
(y+3)(y+6)
$$

Deboney Harris

Numerade Educator

01:04

Problem 89

Multiply. See Section 5.3.
$$
(b+1)(b-4)
$$

Deboney Harris

Numerade Educator

01:17

Problem 90

Multiply. See Section 5.3.
$$
(x-5)(x+10)
$$

Deboney Harris

Numerade Educator

04:06

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you.
$$
\begin{array}{|l|c|c|c|c|c|c|}
\hline & {} & {91 .} & {92 .} & {93 .} & {94 .} & {95 .} & {96 .} \\
\hline \text {Two Numbers } & {4,7} & {} & {} & {} & {} \\
\hline \text {Their Product } & {28} & {12} & {20} & {8} & {16} & {-10} & {-24} \\
\hline \text {Their Sum } & {11} & {8} & {9} & {-9} & {-10} & {3} & {-5} \\
\hline
\end{array}
$$

Elicia Davenport

Numerade Educator

00:59

Problem 92

Deboney Harris

Numerade Educator

01:09

Problem 93

Deboney Harris

Numerade Educator

01:03

Problem 94

Deboney Harris

Numerade Educator

01:23

Problem 95

Deboney Harris

Numerade Educator

01:48

Problem 96

Deboney Harris

Numerade Educator

00:28

Problem 97

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

Numerade Educator

Problem 98

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

Deboney Harris

Numerade Educator

00:28

Problem 99

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

Deboney Harris

Numerade Educator