Free Printable Unit 9 Test Review

1.

Given the graph:

the leading coefficient is.....

a)

Positive

b)

Negative

2.

True or False:

Given the graph, (x + 2) is a factor.

a)

True

b)

False

3.

Given the graph, the constant of the equation in standard form is (a) .

4.

What is the remainder if you synthetically divide $\left(x^4-18x^2+81\right)\div\left(x-2\right)$ ?

(a)

5.

USE THE GRAPH of the function of $f\left(x\right)=x^3+2x^2-x-2$ to write the function in factored form.

Enter your answer with no spaces with no f(x) =

(a)

6.

Find the value of k so that the binomial (x + 2) is a factor of the function $f\left(x\right)=-3x^3+kx-2$ .

Do not enter k = in your answer.

(a)

7.

a)

b)

c)

d)

8.

a)

b)

c)

d)

9.

Simplify: $\left(2x-3\right)\left(x^2+2x\right)-\left(x+3\right)$

a)

$2x^3+x^2-7x-3$

b)

$2x^3-x^2-7x+3$

c)

$x^3+2x^2-7x+3$

d)

$x^3+x^2-7x-3$

10.

Simplify the polynomial: $\left(3x^3-\left(2x\right)^2+5x\right)-\left(x-5x^5+2x\right)$

The function can be classified as _____.

a)

linear

b)

quadratic

c)

cubic

d)

quartic

e)

quintic

11.

Simplify the polynomial: $\left(3x^3-\left(2x\right)^2+5x\right)-\left(x-5x^5+2x\right)$

The leading coefficient is _____.

a)

1

b)

2

c)

3

d)

4

e)

5

12.

Given the graph, what is the multiplicity at x = -4?

(a)

13.

Given the graph, what is the multiplicity at x = -1?

(a)

14.

Classify the function based on the graph:

a)

Linear

b)

Quadratic

c)

Cubic

d)

Quartic

e)

Quintic

15.

Is (x + 2) a factor of the function $x^3+x^2-8x-12$ ?

a)

Yes

b)

No

16.

Is (x - 2) a factor of the function $x^3+x^2-8x-12$ ?

a)

Yes

b)

No

17.

Is (x - 1) a factor of the function $x^3+x^2-8x-12$ ?

a)

Yes

b)

No

18.

Which of the following polynomials is/are completely factored correctly?

Choose ALL that apply.

a)

$x^4-16=\left(x^2-4\right)\left(x^2+4\right)$

b)

$2x^3+2x^2-12x=2x\left(x+3\right)\left(x-2\right)$

c)

$2x^2-2x-24=2\left(x-4\right)\left(x+3\right)$

d)

$16x^3-18=2\left(2a+3\right)\left(2a-3\right)$

19.

A quartic function, h(x), is such that its leading coefficient is -2. Which two of the following would describe the correct end behaviors of the graph of the function?

Choose ALL that apply.

a)

b)

c)

d)

20.

Given the following function, select all that apply: $f\left(x\right)=x^3+6x^2+5x$

a)

x = 0 is a root of f(x)

b)

The range of f(x) = (-∞, ∞)

c)

The graph of f(x) rises to the right and falls to the left.

d)

One of the roots has a multiplicity of 2.

e)

In factored form, f(x) = x(x - 5)(x - 1)

21.

What is the FACTOR, related to the graph, that has a multiplicity of 2?

(a)

22.

Given the graph, select all that are true:

a)

a < 0

b)

The factor (x + 1) is a factor of the function twice.

c)

The value of c in the equation is 4.

d)

The function is cubic.

23.

Given: $g\left(x\right)=3x-1$ $f\left(x\right)=2x^3+x^2-2x+4$ $h\left(x\right)=x+5$

Suppose a function p(x) is defined as $p\left(x\right)=\left[g\left(x\right)\right]^2-f\left(x\right)$ , find the equation for p(x).

What is the coefficient of the

x^3

term?

(a)

24.

Given: $g\left(x\right)=3x-1$ $f\left(x\right)=2x^3+x^2-2x+4$ $h\left(x\right)=x+5$

Suppose a function p(x) is defined as $p\left(x\right)=\left[g\left(x\right)\right]^2-f\left(x\right)$ , find the equation for p(x).

What is the coefficient of the

x^2

term?

(a)

25.

Given: $g\left(x\right)=3x-1$ $f\left(x\right)=2x^3+x^2-2x+4$ $h\left(x\right)=x+5$

Suppose a function p(x) is defined as $p\left(x\right)=\left[g\left(x\right)\right]^2-f\left(x\right)$ , find the equation for p(x).

What is the coefficient of the

x^{ }

term?

(a)

26.

Given: $g\left(x\right)=3x-1$ $f\left(x\right)=2x^3+x^2-2x+4$ $h\left(x\right)=x+5$

Suppose a function p(x) is defined as $p\left(x\right)=\left[g\left(x\right)\right]^2-f\left(x\right)$ , find the equation for p(x).

What is the constant term?

(a)

27.

Given: $g\left(x\right)=3x-1$ $f\left(x\right)=2x^3+x^2-2x+4$ $h\left(x\right)=x+5$

Suppose a function m(x) is defined as $m\left(x\right)=g\left(x\right)+f\left(x\right)\cdot h\left(x\right)$ , find the equation for m(x).

Based on this equation, where should the graph cross the y-axis? Enter your answer as an ordered pair.

(a)

28.

Given: $g\left(x\right)=3x-1$ $f\left(x\right)=2x^3+x^2-2x+4$ $h\left(x\right)=x+5$

Divide f(x) by h(x).

Is h(x) a factor?

a)

Yes

b)

No

29.

The graph of a polynomial function m(x) is pictured. Which of the following equations would be the FACTORED form of m(x)?

a)

$m\left(x\right)=x\left(x+5\right)\left(x+2\right)\left(x-2\right)$

b)

$m\left(x\right)=x\left(x-5\right)\left(x-2\right)\left(x+2\right)$

c)

$m\left(x\right)=x\left(x+5\right)\left(x+2\right)^2$

d)

$m\left(x\right)=x\left(x-5\right)\left(x+2\right)\left(x+2\right)$

30.

The graph of a polynomial function m(x) is pictured. Which of the following equations would be the STANDARD form of m(x)?

a)

$m\left(x\right)=x^4+5x^3-4x^2-20x$

b)

$m\left(x\right)=x^4-5x^3+4x^2+20x$

c)

$m\left(x\right)=-x^4+5x^3-4x^2-20x$

d)

$m\left(x\right)=-x^4-5x^3+4x^2+20x$

31.

If e(x) is represented by the equation below, what is the multiplicity at x = 3? $e\left(x\right)=x\left(x-3\right)^2\left(x+3\right)\left(x+4\right)$

(a)

Unit 9 Test Review

Total questions: 31

Worksheet time: 5hrs 1mins

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