# Prealgebra

## Educators

Problem 1

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.
$$5 x+2$$

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Problem 2

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.
$$z^{2}-5 z-6$$

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Problem 3

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.
$$a^{2}+9 a+18$$

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Problem 4

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.
$$-12 p^{4}$$

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Problem 5

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.
$$y^{3}-8 y^{2}+2 y-16$$

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Problem 6

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.
$$10-9 x$$

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Problem 7

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.
$$23y^{2}$$

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Problem 8

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.
$$m^{4}+4 m^{3}+6 m^{2}+4 m+1$$

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Problem 9

In the following exercises, determine the degree of each polynomial.
$$8 a^{5}-2 a^{3}+1$$

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Problem 10

In the following exercises, determine the degree of each polynomial.
$$5 c^{3}+11 c^{2}-c-8$$

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Problem 11

In the following exercises, determine the degree of each polynomial.
$$3 x-12$$

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Problem 12

In the following exercises, determine the degree of each polynomial.
$$4 y+17$$

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Problem 13

In the following exercises, determine the degree of each polynomial.
$$-13$$

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Problem 14

In the following exercises, determine the degree of each polynomial.
$$-22$$

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Problem 15

In the following exercises, add or subtract the monomials.
$$6 x^{2}+9 x^{2}$$

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Problem 16

In the following exercises, add or subtract the monomials.
$$4 y^{3}+6 y^{3}$$

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Problem 17

In the following exercises, add or subtract the monomials.
$$-12 u+4 u$$

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Problem 18

In the following exercises, add or subtract the monomials.
$$-3 m+9 m$$

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Problem 19

In the following exercises, add or subtract the monomials.
$$5 a+7 b$$

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Problem 20

In the following exercises, add or subtract the monomials.
$$8 y+6 z$$

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Problem 21

In the following exercises, add or subtract the monomials.
$$\text { Add:} 4 a,-3 b,-8 a$$

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Problem 22

In the following exercises, add or subtract the monomials.
$$\text { Add:}4 x, 3 y,-3 x$$

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Problem 23

In the following exercises, add or subtract the monomials.
$$18 x-2 x$$

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Problem 24

In the following exercises, add or subtract the monomials.
$$13 a-3 a$$

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Problem 25

In the following exercises, add or subtract the monomials.
$$\text { Subtract } 5 x^{6} \text { from }-12 x^{6}$$

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Problem 26

In the following exercises, add or subtract the monomials.
$$\text { Subtract } 2p^{4} \text { from }-7 p^{4}$$

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Problem 27

In the following exercises, add or subtract the polynomials.
$$\left(4 y^{2}+10 y+3\right)+\left(8 y^{2}-6 y+5\right)$$

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Problem 28

In the following exercises, add or subtract the polynomials.
$$\left(7 x^{2}-9 x+2\right)+\left(6 x^{2}-4 x+3\right)$$

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Problem 29

In the following exercises, add or subtract the polynomials.
$$\left(x^{2}+6 x+8\right)+\left(-4 x^{2}+11 x-9\right)$$

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Problem 30

In the following exercises, add or subtract the polynomials.
$$\left(y^{2}+9 y+4\right)+\left(-2 y^{2}-5 y-1\right)$$

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Problem 31

In the following exercises, add or subtract the polynomials.
$$\left(3 a^{2}+7\right)+\left(a^{2}-7 a-18\right)$$

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Problem 32

In the following exercises, add or subtract the polynomials.
$$\left(p^{2}-5 p-11\right)+\left(3 p^{2}+9\right)$$

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Problem 33

In the following exercises, add or subtract the polynomials.
$$\left(6 m^{2}-9 m-3\right)-\left(2 m^{2}+m-5\right)$$

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Problem 34

In the following exercises, add or subtract the polynomials.
$$\left(3 n^{2}-4 n+1\right)-\left(4 n^{2}-n-2\right)$$

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Problem 35

In the following exercises, add or subtract the polynomials.
$$\left(z^{2}+8 z+9\right)-\left(z^{2}-3 z+1\right)$$

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Problem 36

In the following exercises, add or subtract the polynomials.
$$\left(z^{2}-7 z+5\right)-\left(z^{2}-8 z+6\right)$$

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Problem 37

In the following exercises, add or subtract the polynomials.
$$\left(12 s^{2}-15 s\right)-(s-9)$$

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Problem 38

In the following exercises, add or subtract the polynomials.
$$\left(10 r^{2}-20 r\right)-(r-8)$$

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Problem 39

In the following exercises, add or subtract the polynomials.
Find the sum of $\left(2 p^{3}-8\right)$ and $\left(p^{2}+9 p+18\right)$

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Problem 40

In the following exercises, add or subtract the polynomials.
Find the sum of $\left(q^{2}+4 q+13\right)$ and $\left(7 q^{3}-3\right)$

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Problem 41

In the following exercises, add or subtract the polynomials.
Subtract $\left(7 x^{2}-4 x+2\right)$ from $\left(8 x^{2}-x+6\right)$

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Problem 42

In the following exercises, add or subtract the polynomials.
Subtract $\left(5 x^{2}-x+12\right)$ from $\left(9 x^{2}-6 x-20\right)$

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Problem 43

In the following exercises, add or subtract the polynomials.
Find the difference of $\left(w^{2}+w-42\right)$ and $\left(w^{2}-10 w+24\right)$

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Problem 44

In the following exercises, add or subtract the polynomials.
Find the difference of $\left(z^{2}-3 z-18\right)$ and $\left(z^{2}+5 z-20\right)$

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Problem 45

In the following exercises, evaluate each polynomial for the given value.
Evaluate $8 y^{2}-3 y+2$
(a) $y=5 \quad$ (b) $y=-2$
(c) $y=0$

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Problem 46

In the following exercises, evaluate each polynomial for the given value.
Evaluate $5 y^{2}-y-7$ when:
(a) $y=-4 \quad$ (b)$y=1$
(c) $y=0$

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Problem 47

In the following exercises, evaluate each polynomial for the given value.
Evaluate $4-36 x$ when:
(a) $x=3 \quad$ (b) $x=0$
(c) $x=-1$

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Problem 48

In the following exercises, evaluate each polynomial for the given value.
Evaluate $16-36 x^{2}$ when:
(a) $x=-1 \quad$ (b) $x=0$
(c) $x=2$

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Problem 49

In the following exercises, evaluate each polynomial for the given value.
A window washer drops a squeegee from a platform 275 feet high. The polynomial $-16 t^{2}+275$ gives the height of the squeegee $t$ seconds after it was dropped. Find the height after $t=4$ seconds.

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Problem 50

In the following exercises, evaluate each polynomial for the given value.
A manufacturer of microwave ovens has found that the revenue received from selling microwaves at a cost of $p$ dollars each is given by the polynomial $-5 p^{2}+350 p$ . Find the revenue received when $p=50$ dollars.

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Problem 51

Fuel Efficiency The fuel efficiency (in miles per gallon) of a bus going at a speed of $x$ miles per hour is given by the polynomial $-\frac{1}{160} x^{2}+\frac{1}{2} x$ . Find the fuel efficiency when $x=40 \mathrm{mph}$ .

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Problem 52

Stopping Distance The number of feet it takes for a car traveling at $x$ miles per hour to stop on dry, level concrete is given by the polynomial $0.06 x^{2}+1.1 x .$ Find the stopping distance when $x=60 \mathrm{mph}$

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Problem 53

Using your own words, explain the difference between a monomial, a binomial, and a trinomial.

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Problem 54

Eloise thinks the sum $5 x^{2}+3 x^{4}$ is 8$x^{6} .$ What is wrong with her reasoning?

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