Free Printable Test 5 Review: Advanced Factoring & Rational Expressions

1.

Factor:
x² - 5x - 14

a)

(x - 2)(x + 3)

b)

(x - 2)(x + 7)

c)

(x + 2)(x - 7)

d)

(x - 2)(x - 3)

2.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

3.

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)

4.

What is the factored form of x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

5.

Factor:
2x² + 11x + 14

a)

(x + 7)(2x + 2)

b)

(x + 2)(2x + 7)

c)

(x + 14)(2x + 1)

d)

(x + 1)(2x + 14)

6.

Factor:
n²+ 10n + 25

a)

(n + 5)(n - 5)

b)

(n + 25)(n + 1)

c)

(n - 5)²

d)

(n + 5)²

7.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

8.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

9.

Simplify

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

10.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

11.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

12.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

13.

Simplify and state the excluded values.

a)

A

b)

B

c)

C

d)

D

14.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

15.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

16.

Simplify

a)

A.(x+7)/(x-4)

b)

B.-3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

17.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

18.

a)

A

b)

B

c)

C

d)

D

19.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

a)

A

b)

B

c)

C

d)

D

25.

a)

A

b)

B

c)

C

d)

D

26.

a)

A

b)

B

c)

C

d)

D

27.

Simplify

a)

A

b)

B

c)

C

d)

D

28.

a)

A

b)

B

c)

C

d)

D

29.

a)

A

b)

B

c)

C

d)

D

30.

Simplify.

a)

A.

b)

B.

c)

C.

d)

D.

31.

Simplify the expression $\frac{x^2-2x-24}{x^2-5x-36}$

a)

$\frac{x-6}{x+9}$

b)

$\frac{x+6}{x+9}$

c)

$\frac{x+6}{x-9}$

d)

$\frac{x-6}{x-9}$

32.

Find the Excluded Value of 32n²/24n

a)

n = 0

b)

n = 24

c)

n = -24

d)

n can be any real number

33.

Given

\frac{\left(x+1\right)\left(x-7\right)}{\left(x-4\right)\left(x+3\right)}

What values will make the rational expression UNDEFINED?

a)

$x=-1,\ x=7$

b)

$x=-1,\ x=4,\ x=7,\ x=-3$

c)

None

d)

$x=4\ ,\ x=-3$

34.

Factor Completely:
x⁴-9x²Hint: Factor GCF first.

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

35.

Simplify $\frac{x^2+x-30}{2x-10}$

a)

$x+3$

b)

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

c)

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

d)

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

36.

x² − 7x − 18

a)

(x − 9)(x + 2)

b)

(x + 9)(x + 2)

c)

(x − 9)(x - 2)

d)

(x − 9)(x - 2)

37.

p² − 5p − 14

a)

( p + 2)( p + 7)

b)

( p + 2)( p − 7)

c)

( p - 2)( p − 7)

d)

( p - 2)( p + 7)

38.

2b² + 17b + 21

a)

(2b + 7)(b + 3)

b)

(2b + 3)(b - 7)

c)

2(b + 3)(b + 7)

d)

(2b + 3)(b + 7)

39.

Reduce, or simplify

the rational expression.

a)

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

b)

( x - 5 ) / ( x - 2 )

c)

( x + 5 ) / ( x - 2 )

d)

-25 / ( 3x - 10 )

40.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

41.

20x³/(5x+10)

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

42.

What type of factoring would you use first?
9x² - 4

a)

Difference of 2 Squares

b)

Difference of 2 Cubes

c)

Sum of 2 Cubes

d)

GCF

43.

7x² − 31x − 20

a)

(7x + 4)(x − 5)

b)

(7x - 4)(x − 5)

c)

(7x + 4)(x + 5)

d)

(7x - 4)(x − 5)

44.

Simplify by cancelling

a)

1

b)

-1

c)

Can't be simplified

45.

x³ + 64

a)

(x + 3)(x² - 3x + 9)

b)

(x + 5)(x² - 5x + 25)

c)

(x + 4)(x² - 4x + 16)

d)

(x - 4)(x² + 4x + 16)

46.

Reduce, or simplify

the algebraic fraction.

a)

x - 3

b)

-21

c)

-3

d)

( x - 3 ) / ( x )

47.

x³ - 27

a)

(x - 4)(x² + 4x + 16)

b)

(x + 3)(x² - 4x + 16)

c)

(x - 1)(x² + 1x + 1)

d)

(x - 3)(x² + 3x + 9)

48.

125x³ - 64

a)

(5x - 4)(25x² + 20x + 16)

b)

(5x + 2)(25x² - 10x + 4)

c)

(3x - 1)(9x² + 3x + 1)

d)

(4x - 3)(16x² + 12x + 9)

49.

x³ - 64

a)

(x - 4)(x² + 4x + 16)

b)

(x - 3)(x² + 3x + 9)

c)

(x - 5)(x² + 5x + 25)

d)

(x + 4)(x² - 4x + 16)

50.

8x³ + 27

a)

(3x - 2)(9x² + 6x + 4)

b)

(3x - 1)(9x² + 3x + 1)

c)

(2x + 3)(4x² - 6x + 9)

d)

(2x - 1)(4x² + 2x + 1)

51.

125x³ + 8

a)

(5x - 4)(25x² + 20x + 16)

b)

(5x + 2)(25x² - 10x + 4)

c)

(4x + 1)(16x² + 4x + 1)

d)

(4x - 3)(16x² + 12x + 9)

52.

What type of factoring would you use first?
3x⁴ - 9x

a)

Difference of 2 Squares

b)

Difference of 2 Cubes

c)

Sum of 2 Cubes

d)

GCF

53.

x³ + 27

a)

(x + 3)(x² - 3x + 9)

b)

(x + 2)(x² - 2x + 4)

c)

(x + 4)(x² - 4x + 16)

d)

(x - 3)(x² + 3x + 9)

54.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Use the X-Puzzle

55.

Which of these can factor using difference of two squares?

a)

144x² - 49y²

b)

x² + 4x - 12

c)

100x² + 20x + 1

d)

14x - 16

56.

Factor 4x²-9

a)

(4x-9)(4x+9)

b)

(2x-3)(2x+3)

c)

2x-3

d)

(2x-4.5)(2x+4.5)

57.

What type of factoring would you use first?
4x³ - 24x

a)

Difference of 2 Squares

b)

Difference of 2 Cubes

c)

Sum of 2 Cubes

d)

GCF

58.

Factor x²-25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

59.

32n² - 50
(Check for a GCF)

a)

(16n - 25)(16n + 25)

b)

2(8n - 25)(8n + 25)

c)

2(4n + 5)(4n - 5)

d)

Not Factorable

60.

Which one is false about the difference of two squares?

a)

We can factor because there is addition sign.

b)

We can factor because there is a perfect squared number (Example: x², 25, 49)

c)

Formula: a² - b² = (a + b) (a - b)

d)

We can factor because there is minus sign.

61.

What type of factoring would you use first?
8x³ - 1

a)

Difference of 2 Squares

b)

Difference of 2 Cubes

c)

Sum of 2 Cubes

d)

GCF

62.

What type of factoring would you use first?
x² - 7x - 8

a)

GCF

b)

(x - ) (x- )

c)

(x+ )(x+ )

d)

(x+ )(x- )

63.

What type of factoring would you use first?
x³ - 1000x

a)

Difference of 2 Squares

b)

Difference of 2 Cubes

c)

Sum of 2 Cubes

d)

GCF

64.

What type of factoring would you use first?
x³ - 1

a)

Difference of 2 Squares

b)

Difference of 2 Cubes

c)

Sum of 2 Cubes

d)

GCF

65.

What type of factoring would you use first?
x³ + 27

a)

Difference of 2 Squares

b)

Difference of 2 Cubes

c)

Sum of 2 Cubes

d)

GCF

66.

What type of factoring would you use first?
16x⁴ - 81

a)

Difference of 2 Squares

b)

Difference of 2 Cubes

c)

Sum of 2 Cubes

d)

GCF

67.

What type of factoring would you use first?
x⁵ - 3x⁴ + 8x³ + 14x²

a)

Grouping

b)

(x - ) (x- )

c)

(x+ )(x+ )

d)

GCF

Test 5 Review: Advanced Factoring & Rational Expressions

Total questions: 67

Worksheet time: 11hrs 10mins

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