Free Printable Polynomials Unit Exam

1.

If you were dividing x⁶ + 4x³ + 2, 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

2.

For synthetic division, what would be the number in the left hand box?

a)

1

b)

-2

c)

2

d)

3

3.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

4.

How could you determine if x-2 is a factor of 2x³-5x²+x-2?

a)

Use synthetic division and see if the quotient is even

b)

Ask the person sitting next to me

c)

Use synthetic division and see if the remainder is zero

d)

Flip a coin

5.

What could be the equation of the polynomial function shown in this graph?

a)

b)

c)

d)

6.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

1, -6, 5

7.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

8.

The degree of a polynomial determines...

a)

the maximum number of x-intercepts

b)

the number of turning points

c)

if the end behavior is up or down

d)

the y-intercept

9.

Identify the zeros:

a)

x = -2, x = -1, x = 0

b)

x = -2, x = 0

c)

x = -1, x = 0, x = 2

d)

x = -2, x = 0, x = 1

10.

What is the increasing interval(s) of the function behind this text?

a)

(-1.3, -.4), (.7, ∞)

b)

(-∞, -5), (.5, 2)

c)

(-5, .5), (2, ∞)

d)

None

11.

SELECT ALL OF THE FOLLOWING intervals over which this function is increasing.

a)

$\left(-\infty;\ -1.6\right)$

b)

$\left(-1.6;\ 0\right)$

c)

$\left(0,\ 0.9\right)$

d)

$\left(0.9;\ \infty\right)$

e)

$\left(-8,\ 3.2\right)$

12.

Where do you find relative minimums and relative maximums?

a)

zeros

b)

y-intercepts

c)

turning points

d)

by degree

13.

$f\left(x\right)=x^3+x^2-24x+36$ has a minimum at which point

a)

(2.5, -2.1)

b)

(2.5, -3.1)

c)

(3.1, -2.1)

d)

(3.1, -2.5)

14.

The given polynomial is decreasing over what interval?

a)

(-3.2, 2.5)

b)

(90.3, -2.1)

c)

(2.5, -3.2)

d)

(-2.1, 90.3)

15.

$f\left(x\right)=x^4-19x^2-6x+72$ has what end behavior?

a)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$As\ x\rightarrow-\infty,\ \ f\left(x\right)\rightarrow\infty$

b)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

c)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty$

d)

$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

16.

Graph the polynomial:

$g\left(x\right)=x^3-7x^2+2x+13$ . What are the interval(s) of increasing and decreasing?

a)

Increasing: (- $\infty$ , 0.148),(4.519, $\infty$ )

Decreasing: (0.148, 4.519)

b)

All real numbers

c)

Increasing: (-1.146, 1.782)

Decreasing: (13.146, -28.627)

d)

Increasing: $\left(-\infty,\ 13.146\right),\left(-28,627,\ \infty\right)$

Decreasing: (13.146, -28.627)

17.

Which of the following is one of the factors of the expression: $4x^2-25?$

a)

$\left(4x-5_{ }\right)$

b)

$\left(2x+1\right)$

c)

$\left(4x-1\right)$

d)

$\left(2x-5\right)$

18.

What is the factored form of the expression? $x^2-16$

a)

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

b)

$\left(x-8\right)\left(x+8\right)$

c)

$\left(x-4\right)\left(x-4\right)$

d)

$\left(x-8\right)\left(x-8\right)$

19.

What are the binomial factors of $x^2+7x-18$

(Pick 2 answers)

a)

$\left(x-9\right)$

b)

$\left(x+9\right)$

c)

$\left(x-2\right)$

d)

$\left(x+2\right)$

20.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

21.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

22.

Complete the formula a³+b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

23.

Simplify this polynomial:

3x²- x + 2 - 5x²+ 8x - 5

a)

8x²+ 9x + 7

b)

-2x²+ 7x - 3

c)

2x²+ 7x - 3

d)

5x²- 3

24.

Which polynomial is written in standard form?

a)

8x - 11x²

b)

4x³ + 7x - 9

c)

12 + 4x

d)

13x + 7x² - 9x³ + 12

25.

What is the constant of this polynomial?

2x³- 8x²+ 3x - 7

a)

2

b)

-8

c)

3

d)

-7

26.

Evaluate
x³ -2x² -17x + 1
for x = -2

a)

19

b)

-33

c)

-49

d)

35

27.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

4

c)

-12

d)

0

28.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x+4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

29.

Which root has even multiplicity?

a)

1

b)

-4

c)

-1

d)

2

30.

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

31.

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

32.

What is the end behavior of a third degree polynomial with a positive leading coefficient?

a)

As x approaches infinity, f(x) approaches infinity. As x approaches negative infinity, f(x) approaches infinity.

b)

As x approaches infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.

c)

As x approaches infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches infinity.

d)

As x approaches infinity, f(x) approaches infinity. As x approaches negative infinity, f(x) approaches negative infinity.

Polynomials Unit Exam

Total questions: 32

Worksheet time: 2hrs 56mins

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