Free Printable Unit 3 Review -Polynomials

1.

Last Name

4 lines

2.

First Name

4 lines

3.

What period do you have Precalculus?

4 lines

4.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

5.

How is the constant term of an equation in standard form related to the graph?

a)

It is the y-intercept

b)

It is the x-intercept

c)

It is the multiplicity

d)

There is no relationship

6.

The degree of the polynomial determines the max number of roots.

a)

True

b)

False

7.

How many roots or zeros does the equation

f(x) = 5x⁴-8x³+4x²-6x+3 have?

a)

3

b)

4

c)

5

d)

0

8.

Is the leading coefficient for the polynomial shown positive or negative?

a)

Negative

b)

Positive

c)

Cannot be determined

9.

What is the degree of the polynomial shown in the image?

a)

4

b)

5

c)

7

d)

6

10.

What is the y-intercept for the polynomial given:

y = 3x² + 9x⁵ − 4 + 10x⁸ + 2x⁹ ?

a)

2

b)

-4

c)

9

d)

3

11.

Which one could be a representation of the equation of this graph?

a)

$-x\left(x-4\right)\left(x+3\right)\left(x+7\right)$

b)

$-x\left(x+4\right)\left(x-3\right)\left(x-7\right)$

c)

$x\left(x-4\right)\left(x+3\right)\left(x+7\right)$

d)

$x\left(x+4\right)\left(x-3\right)\left(x-7\right)$

12.

How are factors related to x-intercepts?

a)

They are the same

b)

They are not related

c)

x-intercepts are found by setting the factors=0

d)

x-intercepts are found by setting x=0

13.

What is the end-behavior of the function $f\left(x\right)=-x^3+2x^2-x-4$ ?

a)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\ and\ \lim_{x\rightarrow\infty}f\left(x\right)=-\infty$

b)

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty\ and\ \lim_{x\rightarrow\infty}f\left(x\right)=-\infty$

c)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\ and\ \lim_{x\rightarrow\infty}f\left(x\right)=\infty$

d)

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty\ and\ \lim_{x\rightarrow\infty}f\left(x\right)=\infty$

14.

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4
Degree: 7

a)

(x + 5)³(x - 9)²(x + 2)(x - 4)

b)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

c)

(x + 5)³(x - 9)²(x + 2)

d)

(x + 5)(x - 9)(x + 2)
(x - 4)

15.

Even Multiplicities have which of the following effects on the x-axis?

a)

touches and bounces back

b)

wiggle

c)

crosses the x-axis

16.

Which of the following is a COMPLETE list of all possible Rational Zeros?

f(x) = 2x³ + 5x² - 9x + 5

a)

±1, ±5, ±1/2, ±5/2

b)

±1, ±5

c)

±1, ±2, ±5, ±1/2, ±5/2

d)

±1, ±2, ±5, ±1/2, ±5/2, ±2/5

17.

Solve by using Rational Root Theorem:

x³ - 7x - 6 = 0

a)

1, 2, 3

b)

-1, -2, 3

c)

-1, -2, - 3

d)

1,-2,-3

18.

If you were dividing x⁶ + 4x³ + 2 by a binomial, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

19.

According to the Rational Root Theorem, what are the all possible rational roots?

2x³ - 11x² + 12x + 9 = 0

a)

±1,±2

b)

±1,±3±9,±1/2,±3/2,±9/2

c)

±1,±3,±9

d)

±1,±2,±1/3,±2/3,±1/9,±2/9

20.

How many positive solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

a)

4, 2, or 0

b)

3 or 1

c)

4

d)

3

21.

How many possible negatives solutions does the following polynomial have?

f(x) = x⁴ - 3x³ - 17x² + 39x -20

a)

3 or 1

b)

3

c)

1

d)

2 or 0

22.

State the number of complex zeros for this function.

a)

7, 5, 3, or 1

b)

4

c)

5

d)

7

23.

Find all zeros.

a)

b)

c)

d)

24.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

a)

b)

c)

d)

25.

Which formula is the Fundamental Theorem of Algebra Formula?

a)

There are infinitely many rationals between two reals.

b)

An nth degree polynomial always has 2 x-intercepts

c)

An nth degree polynomial has n solutions.

Unit 3 Review -Polynomials

Total questions: 25

Worksheet time: 1hrs 22mins

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