Free Printable Review for Test 5.1

1.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

2.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

3.

What can we expect the end behavior to be on the graph of the function: $f\left(x\right)=5x^4-x+6$

a)

Rises on the left and right

b)

Rises on left, falls on right

c)

Falls on the left, rises on the right

d)

Falls on the left and right

4.

What can we expect the end behavior to be on the graph of the function: $f\left(x\right)=2x^3-x+5$

a)

Rises on the left and right

b)

Rises on left, falls on right

c)

Falls on the left, rises on the right

d)

Falls on the left and right

5.

Factor.

6.

If (x+2) is a factor of f(x), then which statement BEST represents f(x)?

a)

x=-2 is a zero of f(x)

b)

x=-2 is not a zero of f(x)

c)

x=2 is a zero of f(x)

d)

x=2 is not a zero of f(x)

7.

$a^3+b^3=$ (a)

Choose from the below words

$\left(a+b\right)\left(a^2-ab+b^2\right)$

$\left(a-b\right)\left(a^2+ab+b^2\right)$

$\left(a+b\right)\left(a^2-ab-b^2\right)$

$\left(a-b\right)\left(a^2-ab-b^2\right)$

8.

$a^3-b^3=$ (a)

Choose from the below words

$\left(a-b\right)\left(a^2+ab+b^2\right)$

$\left(a+b\right)\left(a^2-ab-b^2\right)$

$\left(a-b\right)\left(a^2-ab-b^2\right)$

$\left(a+b\right)\left(a^2+ab+b^2\right)$

9.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

10.

Fully Factor the Following
216x³+125

a)

6(x+5)³

b)

(6x+5)³

c)

(6x+5)(6x²-30x+25)

d)

(6x+5)(36x²-30x+25)

11.

Write a polynomial function of least degree for the given zeros:

a)

A

b)

B

c)

C

d)

D

12.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

*Hint, create three factors, multiply them together.

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

13.

a)

This is correct

b)

This is incorrect

14.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

15.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

16.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

17.

a)

2x - 4

b)

2x + 4

c)

2x - 1 + -16/4x-5

d)

2x - 4 + -40/4x-5

18.

Form the choices, which polynomial function in factored form represents the given graph?

a)

$y=\left(x+2\right)\left(x+1\right)\left(x-1\right)$

b)

$y=\left(x+1\right)\left(x-1\right)\left(x-2\right)$

c)

$y=x\left(x+2\right)\left(x+1\right)\left(x-1\right)$

d)

$y=x\left(x+1\right)\left(x-1\right)\left(x-2\right)$

19.

Now that it is in factored form, what are the zeros?

\left(x-4\right)\left(x+2\right)\left(x-2\right)=0

a)

-2, 2, 4

b)

-2, 2, -4

Review for Test 5.1 - 5.4

Total questions: 19

Worksheet time: 2hrs 46mins

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