# Prealgebra

## Educators ### Problem 1

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

### Problem 2

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

### Problem 3

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

### Problem 4

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

### Problem 5

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

### Problem 6

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

### Problem 7

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

### Problem 8

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

### Problem 9

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

### Problem 10

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

### Problem 11

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

### Problem 12

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

### Problem 13

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

### Problem 14

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

### Problem 15

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

### Problem 16

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

### Problem 17

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

### Problem 18

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

### Problem 19

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

### Problem 20

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

### Problem 21

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

### Problem 22

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

### Problem 23

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

### Problem 24

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

### Problem 25

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

### Problem 26

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

### Problem 27

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

### Problem 28

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

### Problem 29

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

### Problem 30

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

### Problem 31

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

### Problem 32

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

### Problem 33

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

### Problem 34

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

### Problem 35

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

### Problem 36

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

### Problem 37

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

### Problem 38

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

### Problem 39

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

### Problem 40

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

### Problem 41

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

### Problem 42

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

### Problem 43

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

### Problem 44

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

### 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) $y=0$ Cory K.

### 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) $y=0$ Cory K.

### 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) $x=-1$ Cory K.

### 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) $x=2$ Cory K.

### 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. Cory K.

### 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. Cory K.

### 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 $x=40 \mathrm{mph}$ . Cory K.

### 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 $x=60 \mathrm{mph}$ Cory K.

### Problem 53

Using your own words, explain the difference between a monomial, a binomial, and a trinomial. Cory K.
Eloise thinks the sum $5 x^{2}+3 x^{4}$ is 8$x^{6} .$ What is wrong with her reasoning? 