Free Printable Unit 5 Quiz Review

1.

Describe the type of polynomial shown.

a)

Even degree, negative leading coefficient

b)

Odd degree, positive leading coefficient

c)

Odd degree, negative leading coefficient

d)

Even degree, positive leading coefficient

2.

Which of the following is NOT a zero to f(x)=3x(x-8)(x+1)²?

a)

0

b)

-1

c)

1

d)

8

3.

Determine the end behavior of the following function.

y=-7x^3+8x^2+x

a)

Up and Up

b)

Up and Down

c)

Down and Down

d)

Down and Up

4.

Determine the end behavior for the following polynomial.

y=-3\ -6x^5-9x^8

***be careful***

a)

Up and Up

b)

Up and Down

c)

Down and Down

d)

Down and Up

5.

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)

6.

Use the end behavior determined from the equation f(x) = x³ + x² - 4x -4 and the zeros from the equation f(x) = (x+1)(x-2)(x+2) to find the graph of the function (these equations are the same in different forms).

a)

A (up down) (zeros: -2 & 2)

b)

B (down up) (zeros: 0)

c)

C (down up) (zeros: -2, -1, & 2)

d)

D (up up) (zeros: -1 & 5)

7.

The function shown has:

a)

Degree two with positive leading coefficient.

b)

Degree three with negative leading coefficient.

c)

Degree four with negative leading coefficient.

d)

Degree four with positive leading coefficient.

8.

Select all the graphs which show even degree functions.

a)

b)

c)

d)

9.

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

a)

x-intercept

b)

zero

c)

all of these.

10.

Pick all statements that apply to this polynomial.

a)

It is an odd degree function.

b)

It is an even degree function.

c)

It has a positive leading coefficient.

d)

It has a negative leading coefficient.

e)

It has 3 zeros.

11.

Select all statements that apply to this polynomial.

a)

This is an odd degree function.

b)

This is an even degree function.

c)

The leading coefficient is positive.

d)

The leading coefficient is negative.

12.

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, -3, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 3

13.

a)

y = x(x - 3)(x - 2)

b)

y = x(x - 3)²(x+2)

c)

y = x(x + 3)²(x - 2)

d)

y = -x(x + 3)²(x - 2)

14.

Write an equation for a function that has the following characteristics:

*negative leading coefficient

*zero: 7

*multiplicity at zero: two

a)

y = -(x + 7)(x - 7)

b)

y = -(x - 7)²

c)

y = -(x + 7)²

d)

y = -(x - 7)⁴

15.

Which equations best represents the graph?

a)

$f\left(x\right)=\ \left(2-x\right)\left(x-2\right)^2$

b)

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

c)

$h\left(x\right)=\ -\left(x-4\right)^2\left(x+2\right)^{ }$

d)

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

16.

The largest exponent found in the polynomial

a)

Term

b)

Degree

c)

Constant

d)

Leading Coefficient

17.

The coefficient of the first term of a polynomial written in standard form

a)

Term

b)

Degree

c)

Constant

d)

Leading Coefficient

18.

Standard form is arranging the terms of a polynomial in what order?

a)

highest to lowest coefficient

b)

highest to lowest degree

c)

lowest to highest coefficient

d)

lowest to highest degree

19.

Identify the degree of the polynomial

3x⁴ + 2x² - 7

a)

1st degree

b)

2nd degree

c)

3rd degree

d)

4th degree

20.

Identify the degree of the polynomial

5x⁴ - 3x² + 2x⁶ - x + 7

a)

2nd degree

b)

4th degree

c)

5th degree

d)

6th degree

21.

Which of the following polynomials is written in standard form?

a)

9 + 8x - 2x²

b)

10x + x³ - 4x² - 11

c)

x⁴ + 5x³ - 6x +1

d)

4x³+ 3x⁴ + 2x + 1

22.

What is the leading coefficient in the polynomial 3x²- 2x + 5?

a)

3

b)

2

c)

5

d)

0

23.

Which of these is in Standard Form (Check ALL that apply)?

a)

$4x^2+12x-13x^3$

b)

$5-3x$

c)

$2x^4-12x^2+5x-9$

d)

$5x^5+4x^{\text{4}}+12x^3-23x+15$

24.

a)

(-2.55, 0), (2.55, 0)

b)

(-3, 0), (-2, 0), (2, 0), (3, 0)

c)

(0, 36)

d)

(0, -3), (0, -2), (0, 2), (0, 3)

25.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

26.

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

a)

Left side: Rises
Right side: Rises

b)

Left Side: Rises
Right side: Falls

c)

Left side: Falls
Right side: Rises

d)

Left side: Falls
Right side: Falls

27.

Write a 4th degree polynomial function with:
*a positive leading coefficient
*zeros: 9, 3, -2, 0

a)

y = x(x - 9)(x - 3)(x + 2)

b)

y = x(x + 9)(x + 3)(x - 2)

c)

y = -x(x - 9)(x - 3)(x + 2)

d)

y = -x(x + 9)(x + 3)(x - 2)

28.

a)

y = x(x - 3)(x - 2)

b)

y = x(x - 3)²(x+2)

c)

y = x(x + 3)²(x - 2)

d)

y = -x(x + 3)²(x - 2)

29.

f(x) = (x-4)²(x+1)

a)

Even Degree
- Leading Coeff.

b)

Even Degree
+ Leading Coeff.

c)

Odd Degree
- Leading Coeff.

d)

Odd Degree
+ Leading Coeff.

30.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

31.

What is the degree of the function graphed here?

a)

6

b)

4

c)

3

d)

5

32.

What is the y-intercept?
f(x) = -x⁴ + x³ + 5x² + x + 6

a)

-1

b)

1

c)

5

d)

6

33.

What degree is the function?

a)

1

b)

2

c)

4

d)

10

34.

Is the leading coefficient positive or negative

a)

positive

b)

negative

35.

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

a)

{0 mult. 3, 5, 2}

b)

{−2 mult. 3, 3, 1}

c)

{0 mult. 3, 3, 2}

d)

{2 mult. 3, 3, 3}

36.

Even or Odd degree?

a)

even

b)

odd

37.

Which function is graphed?

a)

(x - 4)(x + 2)(x - 8)=y

b)

(x - 4)(x - 2)(x + 8)=y

c)

(x - 4)(x + 2)(x + 8)=y

d)

(x + 4)(x + 2)(x + 8)=y

38.

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

a)

-2, 3 (multiplicity 2), 4

b)

-2 (multiplicity 2), 3, 4

c)

2, -3 (multiplicity 2), -4

d)

2 (multiplicity 2), -3, -4

39.

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

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)

40.

How many zeros do you see that "bounce off" the x-axis?

a)

1

b)

2

c)

3

d)

4

41.

What degree is most likely represents the graph?

a)

linear

b)

quadratic

c)

cubic

d)

quartic

42.

What are the zeros?

a)

x = - 4

b)

There are none

c)

x = - 1.5 & 1.5

d)

x = - 3.5 and 3.5

43.

What are the zeros of the graph?

a)

-4, -1, 2, 1 multiplicity 2

b)

-4, -1, 1, 2

c)

4, 1, -2, -1 multiplicity 2

d)

4, 1, -1, -2

44.

What are the zeros of the function shown?

a)

{-2, 1, 2}

b)

{-3, 1, 2}

c)

{-4, 2, 5}

d)

{-4, 3, 4}

45.

a)

2

b)

1

c)

4

d)

None

46.

Identify the zeros:

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

47.

What are the zeros of the function?

a)

4, 1

b)

-3, -1, 2, 5

c)

-3, -1, 30, 2, 5

d)

3, 1, -2, -5

48.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

49.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

50.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

51.

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

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

52.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

53.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

54.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

55.

Using Synthetic Division; $\left(2x^3+6x^2-6\right)\div\left(x+3\right)$ , specifically, which answer is the remainder correctly represented below?

a)

2x+6

b)

2x-6

c)

$2x^2+\frac{6}{x+3}$

d)

$2x^2-\frac{6}{x+3}$

56.

x³-3x²-10x+24 ÷ x+3

a)

x²-7x+5

b)

x-8

c)

x²-6x+8

d)

x+9

57.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

58.

4x⁴+4x³-9x²-x+2 ÷ x-1

a)

4x³+8x²-7x-2

b)

4x³+19x²-x-2

c)

4x³+8x²-x-9

d)

4x³+8x²-x-2

59.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

$2x^2-x+1+\frac{9}{x-2}$

d)

$2x^2-9x-15-\frac{23}{x-2}$

60.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

61.

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

62.

Using synthetic division, find the remaining factors of

(x³ +x² -17x +15) if (x -1) is a factor?

*FACTOR COMPLETELY*

a)

(x + 5)(x - 3)

b)

(x + 5)(x + 3)

c)

(x - 5)(x + 3)

d)

(x - 5)(x - 3)

63.

Find all the real zeros of the function
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

a)

x = 1/2, -6

b)

x = -1/2, 6

c)

x = 4, -1/2, 6

d)

x = -4, 1/2, -6

64.

Factor:
x³-12x²+47x-60=0 when 5 is a root.

a)

(x-3)(x-4)(x-5)=0

b)

(x+1)(x-4)(x-5)=0

c)

(x-3)(x-4)(2x-5)=0

d)

(x-5)(x-4)(x-5)=0

65.

Find all rational zeros, one zero has been given.
f(x) = x³-3x²-x+3; 3

a)

2,4,3

b)

-1,1,3

c)

3,2,1

d)

4,5,6

66.

Find all rational zeros, one zero has been given.
f(x) = x³-5x²-2x+24; -2

a)

-2,1,0

b)

-2,-3,-4

c)

4,3,-2

d)

0,0,0

67.

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

68.

Factor f(x)= x³ - 2x²-13x - 10 given that
(x - 5) is one factor.

a)

(x- 5)(x - 1)(x - 2)

b)

(x - 5)(x + 2)(x - 2)

c)

(x - 5)(x + 2) (x + 1)

d)

(x - 5)(2x - 13)

69.

Find all zeroes given a factor of (x+3).

f(x) = 2x³+ 5x²- 6x - 9

a)

-1,-3,-3

b)

-1,-3,3/2

c)

3,3,3

d)

-3,2/3,-1

70.

Find all solutions, one factor has been given.

f(x) =x³-3x²-25x+75; (x-5)

a)

5,-3,5

b)

5,5,5

c)

3,-5,5

d)

1,1,1

Unit 5 Quiz Review

Total questions: 70

Worksheet time: 6hrs 50mins

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