Free Printable Module 3 Review

1.

Which of the following is the graph of $y=\left(x-2\right)^3-4$

a)

b)

c)

d)

2.

Which of the following is the graph of $y=\left(x+5\right)^3-1$

a)

b)

c)

d)

3.

Which of the following is the equation for the cubic function graphed above

a)

$y=\left(x+4\right)^3+3$

b)

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

c)

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

d)

$y=\left(x-4\right)^3-3$

4.

Which of the following is the equation of the cubic function graphed above

a)

$y=-\left(x-1\right)^3+4$

b)

$y=\left(x-1\right)^3+4$

c)

$y=-\left(x+1\right)^3+4$

d)

$y=\left(x+1\right)^3+4$

5.

The graph of a function is shown. What are the domain and range of this function?

a)

Domain: (-∞, ∞)
Range: (-∞, 2]

b)

Domain: [2, ∞)
Range: (-∞, ∞)

c)

Domain: (-∞, ∞)
Range: (-∞, ∞)

d)

Domain: (-∞, 2]
Range: [2, ∞)

6.

What is the equation of this function?

a)

f(x) = (x + 2)³

b)

f(x) = (x - 2)³

c)

f(x) = ∛(x + 2)

d)

f(x) = ∛(x - 2)

7.

Describe the transformation of the graph y = (x)³ + 6

a)

Right 6

b)

Left 6

c)

Up 6

d)

Down 6

8.

What is the equation of the graph shown?

a)

y= (x-2)³ + 4

b)

y= (x+2)³+ 4

c)

y = - (x-2)³+ 4

d)

y= - (x+2)³ + 4

9.

What is the Domain of ALL Cube Root Functions in interval notation?

a)

(−∞,∞)

b)

−∞<x<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

10.

Solve for x:

(3x + 1)³ = 64

a)

-1

b)

6

c)

1

d)

No real solution

11.

$\left(x+7\right)^3+8=16$

a)

5

b)

505

c)

-505

d)

-5

e)

None

12.

x³ = -8

a)

2

b)

-2

c)

-2,2

d)

2.83

13.

k³ = -1000

a)

-10,10

b)

10

c)

-10

d)

100

14.

4g³ = 500

a)

22.36

b)

125

c)

-5

d)

5

15.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

16.

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

17.

2x³-8x²-x+4

a)

(2x²-1)(x-4)

b)

2(x²-1)(x+4)

c)

(x²-1)(2x-4)

d)

(2x²+1)(x-4)

18.

x³-5x²+5x-25

a)

(x²-5)(x-5)

b)

(x²+5)(x-5)

c)

(x²+5)(x+5)

d)

(x²-1)(x-25)

19.

30x³+15x²-18x-9

a)

(5x²-3)(6x+1)

b)

(5x²-3)(6x+3)

c)

3(5x²+3)(2x-1)

d)

3(5x²-3)(2x+1)

20.

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)

21.

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)

22.

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)

23.

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)

24.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

25.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

26.

Which number is both a perfect square and a perfect cube?

a)

64

b)

27

c)

81

d)

16

27.

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

a)

No

b)

Yes

c)

Yes, getting GCF first

d)

It is a sum of squares

28.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

29.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

30.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

31.

a)

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

b)

x - 8

c)

x - 5 + (3/2x - 4)

d)

x + 5

32.

The answer to a division problem is known as the...?

a)

product

b)

sum

c)

difference

d)

quotient

33.

What does it mean to be a factor of a number?

a)

Divides evenly with a remainder of zero.

b)

Divides unevenly with a remainder of 1.

34.

If you are missing a term in your polynomials (both dividend and divisor), you must put a zero as a coefficient place holder for that term.

a)

True

b)

False

c)

Only for the dividend

d)

Only for the divisor

35.

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

a)

0

b)

-3

c)

9

d)

5

36.

When p(x) = 9x⁴- 45x³+ 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

a)

p(2) = 656

b)

p(2) = 652

c)

p(2) = -64

d)

p(2) = -368

37.

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

38.

What is the quotient when (10n²- 37n - 12) is divided by (n - 4)?

a)

(10n - 3)

b)

(3n - 10)

c)

(10n + 3)

d)

(3n + 10)

39.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

40.

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

41.

a)

2x - 5

b)

x - 4 + (3/4x - 5)

c)

2x + 4 + (3/4x - 5)

d)

2x + 4

42.

Use Long division to divide $\left(x^4\ +\ 7x^3\ +\ 17x^2\ +\ 20x\right)\div\left(x^2\ +\ 4\right)$

a)

$x^2\ +\ 13x\ +\ 7\ +\frac{-52}{x^2+4}$

b)

$x^2\ +\ 7x\ +\frac{13-8}{x^2+4}$

c)

$x^2\ +\ 7x\ \ +13+\frac{-8x-52}{x^2+4}$

d)

$x^2\ +\ 1\ +\frac{1}{x^2+4}$

43.

$\left(3x^3-4x^2-x+1\right)\div\left(x+1\right)$

A student is trying to use long division to solve the problem above. What value should go in the box next?

a)

-2x

b)

2x

c)

-7x

d)

7x

44.

Determine if (x-5) is a factor of $x^4+x^3-25x^2-25x$

a)

yes

b)

no

45.

Determine if (x+4) is a factor of $x^3+3x^2+2x$

a)

yes

b)

no

46.

If a zero has an even multiplicity, the function ___________ at that zero.

a)

passes through the x-axis

b)

bounces

c)

does nothing

47.

If a zero has an odd multiplicity, the function ___________ at that zero.

a)

passes through the x-axis

b)

bounces

c)

does nothing

48.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

49.

What are the

zeros of the polynomial

y = 5(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, 5, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 5

50.

What are the zeros of the polynomial function?

y = 3x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

3, 6, -5

51.

What are the zeros 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

52.

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

a)

Cross the x-axis

b)

Tangent to the x-axis

53.

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

54.

What is the degree of the function graphed here?

a)

2

b)

3

c)

4

d)

5

55.

Which of the following is a 5th degree trinomial with a leading coefficient of -2?

a)

$-2x^5+3x-1$

b)

$5x^{-2}+3x-1$

c)

$-2x^5+3x^{14}+2x^3+x^2-10$

d)

$-2x+5$

56.

What's another word for 'x-intercept'?

a)

domain

b)

multiplicity

c)

real zero

d)

zero

57.

How many real zeros are shown in the graph?

a)

1

b)

2

c)

3

d)

4

58.

How many real zeros are shown in the picture?

a)

0

b)

1

c)

2

d)

3

59.

Which function is a polynomial?

a)

b)

c)

d)

60.

Which graph is NOT a polynomial function?

a)

b)

c)

d)

61.

Find the correct statement about the zeros.

a)

−5 is a zero with multiplicity 1

b)

−5 is a zero with multiplicity 2

c)

−2 is a zero with multiplicity 1

d)

2 is a zero with multiplicity 2

62.

Find the incorrect statement

a)

This function crosses the x-axis at 3

b)

This function is tangent to the x-axis at −4

c)

This function crosses the x-axis at −2

d)

This function crosses the x-axis at 1

63.

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

a)

0

b)

10

c)

15

d)

-7

64.

Which term is missing in this problem?
(2x³ + 5x² + 9) ÷
(x + 3)

a)

x⁴

b)

x³

c)

x²

d)

x

65.

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

a)

-1,-3,-3

b)

-1,-3,3/2

c)

3,3,3

d)

-3,2/3,-1

Module 3 Review

Total questions: 65

Worksheet time: 4hrs 13mins

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