Intermediate Algebra

Jerome E. Kaufmann, Karen L. Schwitters

Chapter 3 Polynomials - all with Video Answers

Educators

+ 3 more educators

Section 1

Polynomials: Sums and Differences

00:35

Problem 1

Answer true or false.
The degree of the monomial $4 x^{2} y$ is 3 .

Adithya Ramanujam

Numerade Educator

00:23

Problem 1

Determine the degree of the given polynomials.
$$
7 x y+6 y
$$

Kristen Tumminia

Numerade Educator

02:01

Problem 2

Answer true or false.
The degree of the polynomial $2 x^{4}-5 x^{3}+7 x^{2}-4 x+6$ is 10 .

Ankit Gupta

Numerade Educator

00:29

Problem 2

Determine the degree of the given polynomials.
$$
-5 x^{2} y^{2}-6 x y^{2}+x
$$

Kristen Tumminia

Numerade Educator

00:29

Problem 3

Determine the degree of the given polynomials.
$$
-x^{2} y+2 x y^{2}-x y
$$

Kristen Tumminia

Numerade Educator

02:01

Problem 3

Answer true or false.
The degree of the polynomial $2 x^{4}-5 x^{3}+7 x^{2}-4 x+6$ is 10 .

Ankit Gupta

Numerade Educator

01:19

Problem 4

Answer true or false.
A polynomial is a monomial or a finite sum of monomials.

Kian Manafi

Numerade Educator

01:20

Problem 5

Answer true or false.
Monomial terms must have whole number exponents for each variable.

Ankit Gupta

Numerade Educator

00:19

Problem 5

Determine the degree of the given polynomials.
$$
5 x^{2}-7 x-2
$$

Kristen Tumminia

Numerade Educator

00:20

Problem 6

Determine the degree of the given polynomials.
$$
7 x^{3}-2 x+4
$$

Jennifer Stoner

Numerade Educator

02:32

Problem 6

Answer true or false.
The sum of $-2 x-1,-x+4,$ and $5 x-7$ is $8 x-4$

Ankit Gupta

Numerade Educator

00:26

Problem 7

Answer true or false.
If $3 x-4$ is subtracted from $-7 x+2,$ the result is $-10 x+6$.

Maninder Singh

Numerade Educator

00:19

Problem 7

Determine the degree of the given polynomials.
$$
8 x^{6}+9
$$

Kristen Tumminia

Numerade Educator

01:50

Problem 8

Answer true or false.
Polynomials must be of the same degree if they are to be added.

Julie Silva

Numerade Educator

00:26

Problem 8

Determine the degree of the given polynomials.
$$
5 y^{6}+y^{4}-2 y^{2}-8
$$

Kristen Tumminia

Numerade Educator

01:01

Problem 9

Answer true or false.
If $-x-1$ is subtracted from the sum of $2 x-1$ and $-4 x-6,$ the result is $-x-6$.

Ankit Gupta

Numerade Educator

00:18

Problem 9

Determine the degree of the given polynomials.
$$
-12
$$

Kristen Tumminia

Numerade Educator

02:32

Problem 10

Answer true or false.
We can form the opposite of a polynomial by taking the opposite of each term.

Yujie Wang

College of San Mateo

00:22

Problem 10

Determine the degree of the given polynomials.
$$
7 x-2 y
$$

Kristen Tumminia

Numerade Educator

00:39

Problem 11

Add the given polynomials.
$3 x-7$ and $7 x+4$

Kristen Tumminia

Numerade Educator

00:42

Problem 12

Add the given polynomials.
$9 x+6$ and $5 x-3$

Kristen Tumminia

Numerade Educator

01:07

Problem 13

Add the given polynomials.
$-5 t-4$ and $-6 t+9$

Jennifer Stoner

Numerade Educator

00:54

Problem 14

Add the given polynomials.
$-7 t+14$ and $-3 t-6$

Kristen Tumminia

Numerade Educator

01:05

Problem 15

Add the given polynomials.
$3 x^{2}-5 x-1$ and $-4 x^{2}+7 x-1$

Kristen Tumminia

Numerade Educator

00:35

Problem 16

Add the given polynomials.
$6 x^{2}+8 x+4$ and $-7 x^{2}-7 x-10$

Jennifer Stoner

Numerade Educator

00:43

Problem 17

Add the given polynomials.
$12 a^{2} b^{2}-9 a b$ and $5 a^{2} b^{2}+4 a b$

Emily Himsel

Numerade Educator

00:42

Problem 18

Add the given polynomials.
$15 a^{2} b^{2}-a b$ and $-20 a^{2} b^{2}-6 a b$

Emily Himsel

Numerade Educator

00:55

Problem 19

Add the given polynomials.
$2 x-4,-7 x+2,$ and $-4 x+9$

Kristen Tumminia

Numerade Educator

00:57

Problem 20

Add the given polynomials.
$-x^{2}-x-4,2 x^{2}-7 x+9,$ and $-3 x^{2}+6 x-10$

Jennifer Stoner

Numerade Educator

01:20

Problem 21

Subtract the polynomials using the horizontal format.
$$
5 x-2 \text { from } 3 x+4
$$

Kristen Tumminia

Numerade Educator

00:55

Problem 22

Subtract the polynomials using the horizontal format.
$$
7 x+5 \text { from } 2 x-1
$$

Jennifer Stoner

Numerade Educator

01:08

Problem 23

Subtract the polynomials using the horizontal format.
$$
-4 a-5 \text { from } 6 a+2
$$

Jennifer Stoner

Numerade Educator

00:27

Problem 24

Subtract the polynomials using the horizontal format.
$$
5 a+7 \text { from }-a-4
$$

Jennifer Stoner

Numerade Educator

00:46

Problem 25

Subtract the polynomials using the horizontal format.
$$
3 x^{2}-x+2 \text { from } 7 x^{2}+9 x+8
$$

Jennifer Stoner

Numerade Educator

00:47

Problem 26

Subtract the polynomials using the horizontal format.
$$
5 x^{2}+4 x-7 \text { from } 3 x^{2}+2 x-9
$$

Jennifer Stoner

Numerade Educator

00:49

Problem 27

Subtract the polynomials using the horizontal format.
$$
2 a^{2}-6 a-4 \text { from }-4 a^{2}+6 a+10
$$

Jennifer Stoner

Numerade Educator

00:45

Problem 28

Subtract the polynomials using the horizontal format.
$$
2 a^{2}-6 a-4 \text { from }-4 a^{2}+6 a+10
$$

Jennifer Stoner

Numerade Educator

01:06

Problem 29

Subtract the polynomials using the horizontal format.
$$
2 x^{3}+x^{2}-7 x-2 \text { from } 5 x^{3}+2 x^{2}+6 x-13
$$

Jennifer Stoner

Numerade Educator

01:06

Problem 30

Subtract the polynomials using the horizontal format.
$$
6 x^{3}+x^{2}+4 \text { from } 9 x^{3}-x-2
$$

Jennifer Stoner

Numerade Educator

00:53

Problem 31

Subtract the polynomials using the vertical format.
$$
5 x-2 \text { from } 12 x+6
$$

Jennifer Stoner

Numerade Educator

00:56

Problem 32

Subtract the polynomials using the vertical format.
$$
3 x-7 \text { from } 2 x+1
$$

Jennifer Stoner

Numerade Educator

00:42

Problem 33

Subtract the polynomials using the vertical format.
$$
-4 x+7 \text { from }-7 x-9
$$

Jennifer Stoner

Numerade Educator

00:32

Problem 34

Subtract the polynomials using the vertical format.
$$
-6 x-2 \text { from } 5 x+6
$$

Jennifer Stoner

Numerade Educator

00:43

Problem 35

Subtract the polynomials using the vertical format.
$$
2 x^{2}+x+6 \text { from } 4 x^{2}-x-2
$$

Jennifer Stoner

Numerade Educator

00:59

Problem 36

Subtract the polynomials using the vertical format.
$$
4 x^{2}-3 x-7 \text { from }-x^{2}-6 x+9
$$

Jennifer Stoner

Numerade Educator

01:01

Problem 37

Subtract the polynomials using the vertical format.
$$
x^{3}+x^{2}-x-1 \text { from }-2 x^{3}+6 x^{2}-3 x+8
$$

Jennifer Stoner

Numerade Educator

01:18

Problem 38

Subtract the polynomials using the vertical format.
$$
2 x^{3}-x+6 \text { from } x^{3}+4 x^{2}+1
$$

Jennifer Stoner

Numerade Educator

00:51

Problem 39

Subtract the polynomials using the vertical format.
$$
-5 x^{2}+6 x-12 \text { from } 2 x-1
$$

Jennifer Stoner

Numerade Educator

01:32

Problem 40

Subtract the polynomials using the vertical format.
$$
2 x^{2}-7 x-10 \text { from }-x^{3}-12
$$

Jennifer Stoner

Numerade Educator

02:21

Problem 41

Perform the operations as described.
Subtract $2 x^{2}-7 x-1$ from the sum of $x^{2}+9 x-4$ and $-5 x^{2}-7 x+10$

Jennifer Stoner

Numerade Educator

02:18

Problem 42

Perform the operations as described.
Subtract $4 x^{2}+6 x+9$ from the sum of $-3 x^{2}-9 x+6$ and $-2 x^{2}+6 x-4$

Jennifer Stoner

Numerade Educator

02:00

Problem 43

Perform the operations as described.
Subtract $-x^{2}-7 x-1$ from the sum of $4 x^{2}+3$ and $-7 x^{2}+2 x$

Jennifer Stoner

Numerade Educator

01:50

Problem 44

Perform the operations as described.
Subtract $-4 x^{2}+6 x-3$ from the sum of $-3 x+4$ and $9 x^{2}-6$

Jennifer Stoner

Numerade Educator

01:53

Problem 45

Perform the operations as described.
Subtract the sum of $5 n^{2}-3 n-2$ and $-7 n^{2}+n+2$ from $-12 n^{2}-n+9$

Jennifer Stoner

Numerade Educator

02:29

Problem 46

Perform the operations as described.
Subtract the sum of $-6 n^{2}+2 n-4$ and $4 n^{2}-2 n+4$ from $-n^{2}-n+1$.

Jennifer Stoner

Numerade Educator

01:08

Problem 47

Perform the indicated operations.
$$
(5 x+2)+(7 x-1)+(-4 x-3)
$$

Jennifer Stoner

Numerade Educator

00:57

Problem 48

Perform the indicated operations.
$$
(-3 x+1)+(6 x-2)+(9 x-4)
$$

Jennifer Stoner

Numerade Educator

00:41

Problem 49

Perform the indicated operations.
$$
(12 x-9)-(-3 x+4)-(7 x+1)
$$

Jennifer Stoner

Numerade Educator

00:44

Problem 50

Perform the indicated operations.
$$
(6 x+4)-(4 x-2)-(-x-1)
$$

Jennifer Stoner

Numerade Educator

01:07

Problem 51

Perform the indicated operations.
$$
\left(2 x^{2}-7 x-1\right)+\left(-4 x^{2}-x+6\right)+\left(-7 x^{2}-4 x-1\right)
$$

Jennifer Stoner

Numerade Educator

01:32

Problem 52

Perform the indicated operations.
$$
\left(5 x^{2}+x+4\right)+\left(-x^{2}+2 x+4\right)+\left(-14 x^{2}-x+6\right)
$$

Nick Johnson

Numerade Educator

01:40

Problem 53

Perform the indicated operations.
$$
\left(7 x^{2}-x-4\right)-\left(9 x^{2}-10 x+8\right)+\left(12 x^{2}+4 x-6\right)
$$

Nicole Hoffman

Numerade Educator

01:09

Problem 54

Perform the indicated operations.
$$
\left(-6 x^{2}+2 x+5\right)-\left(4 x^{2}+4 x-1\right)+\left(7 x^{2}+4\right)
$$

Nicole Hoffman

Numerade Educator

01:11

Problem 55

Perform the indicated operations.
$$
\left(n^{2}-7 n-9\right)-(-3 n+4)-\left(2 n^{2}-9\right)
$$

Nicole Hoffman

Numerade Educator

01:04

Problem 56

Perform the indicated operations.
$$
\left(6 n^{2}-4\right)-\left(5 n^{2}+9\right)-(6 n+4)
$$

Nicole Hoffman

Numerade Educator

01:20

Problem 57

Simplify by removing the inner parentheses first and working outward.
$$
3 x-[5 x-(x+6)]
$$

Vysakh M

Numerade Educator

01:21

Problem 58

Simplify by removing the inner parentheses first and working outward.
$$
7 x-[2 x-(-x-4)]
$$

Vysakh M

Numerade Educator

01:11

Problem 59

Simplify by removing the inner parentheses first and working outward.
$$
2 x^{2}-\left[-3 x^{2}-\left(x^{2}-4\right)\right]
$$

Vysakh M

Numerade Educator

01:13

Problem 60

Simplify by removing the inner parentheses first and working outward.
$$
2 x^{2}-\left[-3 x^{2}-\left(x^{2}-4\right)\right]
$$

Vysakh M

Numerade Educator

01:25

Problem 61

Simplify by removing the inner parentheses first and working outward.
$$
-2 n^{2}-\left[n^{2}-\left(-4 n^{2}+n+6\right)\right]
$$

Nicole Hoffman

Numerade Educator

03:33

Problem 62

Simplify by removing the inner parentheses first and working outward.
$$
-7 n^{2}-\left[3 n^{2}-\left(-n^{2}-n+4\right)\right]
$$

Dr Harish Viswanathan

Numerade Educator

02:01

Problem 63

Simplify by removing the inner parentheses first and working outward.
$$
\left[4 t^{2}-(2 t+1)+3\right]-\left[3 t^{2}+(2 t-1)-5\right]
$$

Nicole Hoffman

Numerade Educator

01:35

Problem 64

Simplify by removing the inner parentheses first and working outward.
$$
-\left(3 n^{2}-2 n+4\right)-\left[2 n^{2}-\left(n^{2}+n+3\right)\right]
$$

Nicole Hoffman

Numerade Educator

View

Problem 65

Simplify by removing the inner parentheses first and working outward.
$$
\left[2 n^{2}-\left(2 n^{2}-n+5\right)\right]+\left[3 n^{2}+\left(n^{2}-2 n-7\right)\right]
$$

Nicole Hoffman

Numerade Educator

01:19

Problem 66

Simplify by removing the inner parentheses first and working outward.
$$
3 x^{2}-\left[4 x^{2}-2 x-\left(x^{2}-2 x+6\right)\right]
$$

Nicole Hoffman

Numerade Educator

View

Problem 67

Simplify by removing the inner parentheses first and working outward.
$$
[7 x y-(2 x-3 x y+y)]-[3 x-(x-10 x y-y)]
$$

Nicole Hoffman

Numerade Educator

View

Problem 68

Simplify by removing the inner parentheses first and working outward.
$$
[9 x y-(4 x+x y-y)]-[4 y-(2 x-x y+6 y)]
$$

Nicole Hoffman

Numerade Educator

View

Problem 69

Simplify by removing the inner parentheses first and working outward.
$$
[9 x y-(4 x+x y-y)]-[4 y-(2 x-x y+6 y)]
$$

Nicole Hoffman

Numerade Educator

01:58

Problem 70

Simplify by removing the inner parentheses first and working outward.
$$
\left[x^{3}-\left(x^{2}-x+1\right)\right]-\left[-x^{3}+\left(7 x^{2}-x+10\right)\right]
$$

Nicole Hoffman

Numerade Educator

01:45

Problem 71

Use geometry to solve the problems.
Find a polynomial that represents the perimeter of each of the following figures (Figures $3.2,3.3,$ and 3.4 ).

Nicole Hoffman

Numerade Educator

03:27

Use geometry to solve the problems.
Find a polynomial that represents the total surface area of the rectangular solid in Figure 3.5 .
Now use that polynomial to determine the total surface area of each of the following rectangular solids.
(a) 3 by 5 by $\underline{4}$
(b) 3 by 5 by $\underline{\text { z }}$
(c) 3 by 5 by $\underline{11}$
(d) 3 by 5 by $\underline{13}$

Elizabeth Waters

Numerade Educator

03:15

Problem 73

Use geometry to solve the problems.
Find a polynomial that represents the total surface area of the right circular cylinder in Figure $3.6 .$ Now use that polynomial to determine the total surface area of each of the following right circular cylinders that have a base with a radius of $4 .$ Use 3.14 for $\pi,$ and express the answers to the nearest tenth.
(a) $h=5$
(b) $h=7$
(c) $h=14$
(d) $h=18$

Elizabeth Waters

Numerade Educator

01:45