Free Printable Factoring Review

1.

$x^4-81$

a)

$\left(x^2-9\right)\left(x^2+9\right)$

b)

$\left(x^2+9\right)\left(x-3\right)\left(x+3\right)$

c)

$\left(x^4-9\right)\left(x^4+9\right)$

d)

$\left(x^2-9\right)\left(x^2-9\right)$

2.

Factor:

64 - 27a³

a)

(4-3a)(9a²+12a+16)

b)

(3a-4)(3a²+12a+16)

c)

(4-3a)(3a²+12a+16)

d)

(4-3a)³

3.

Factor:

x³ - 343

a)

(x + 7) (x² - 7x + 49)

b)

(x² + 1) (x - 343)

c)

(x - 7) (x² + 7x + 49)

d)

(x² - 343) (x + 1)

4.

Factor:

4x² - 25

a)

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

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

5.

Factor completely.
3x²- 9x -120

a)

3(x - 8)(x + 5)

b)

3(x + 8)(x - 5)

c)

(3x + 8)(x - 5)

d)

(3x - 8)(x + 5)

6.

Factor:

25x² - 36y²

a)

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

b)

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

c)

(5x + 6y)²

d)

(5x - 6y)²

7.

Factor Completely:
2k²-14k-60

a)

2(k-10)(k-3)

b)

Not Factorable

c)

(k-5)(k+9)

d)

2(k-10)(k+3)

8.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

9.

Factor completely.
3x² + 10x - 8

a)

(3x + 2)(x + 4)

b)

(7x + 5)(x + 2)

c)

(3x - 2)(x + 4)

d)

(7x - 3)(x - 4)

10.

Which of the following is a factor of 3x² - 7x + 2?

a)

x - 1

b)

x - 2

c)

3x - 2

d)

3x + 1

11.

Factor
v² - 6v + 9

a)

(v-3)²

b)

(v-6)²

c)

(v-9)(v+6)

d)

not factorable

12.

Factor:
2x² - 3x - 2

a)

(2x - 2)(x + 1)

b)

(2x + 1)(x - 2)

c)

(2x - 1)(x - 2)

d)

(2x - 1) (x - 1)

13.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

14.

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)

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.

Which answer choice lists all the factors for 27?

a)

3, 9

b)

1, 3, 9, 27

c)

1, 3, 6, 9, 12, 27

17.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

18.

Factor 4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

19.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

20.

x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

21.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

22.

Which is another way of correctly expressing
(x - 3)(x - 3)?

a)

(x² - 3²)

b)

(x² - 3)

c)

(x + 3)(x - 3)

d)

(x - 3)²

23.

Factor
4x²-25x+25

a)

4(x-5)(x+5)

b)

(x+5)(4x+5)

c)

(x-5)(4x-5)

d)

(x+2)(9x+1)

24.

Factor completely. (Hint: Factor out GCF first.)

18x² - 50

a)

2 ( 9x² - 25 )

b)

( 3x + 5 ) ( 3x - 5 )

c)

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

d)

2 ( 3x - 5 ) ( 3x - 5 )

25.

We can't factor using difference of two square this

49x² + 4y². Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

26.

Which of these can factor using difference of two squares?

a)

144x² - 49y²

b)

x² + 4x - 12

c)

100x² + 20x + 1

d)

14x - 16

27.

Factor completely:
6x² - 13x + 6

a)

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

b)

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

c)

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

d)

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

28.

Factor by grouping:
2x³ + 4x² - 3x - 6

a)

(2x² - 3)(x + 2)

b)

(x² + 2)(2x + 3)

c)

(2x² + 3)(x - 2)

d)

(x² + 2)(2x - 3)

29.

Factor:
9y² - 16

a)

(9y - 4)(y + 4)

b)

(3y + 4)²

c)

(3y - 4)²

d)

(3y + 4)(3y - 4)

30.

Factor. $70x^2-89x-33$

a)

(5x - 11)(14x + 3)

b)

(7x + 1)(10x - 33)

c)

(10x + 3)(7x - 11)

d)

(2x - 3)(35x + 11)

31.

What is the factored form of $x^4+16x+15$

a)

$\left(x^2+15\right)\left(x^2+1\right)$

b)

$\left(x^2+3\right)\left(x^2+5\right)$

c)

$\left(x^2+15\right)\left(x^{ }+1\right)\left(x-1\right)$

d)

$\left(x^2+4\right)\left(x^2+11\right)$

32.

What is the factored form of $3x^4-18x^2+15$

a)

$3\left(x^2-5\right)\left(x^2-3\right)$

b)

$3\left(x^2+45\right)\left(x^2+1\right)$

c)

$3\left(x^2+5\right)\left(x^{ }+3\right)\left(x-3\right)$

d)

$\left(3x^2-15\right)\left(x^2-3\right)$

33.

Complete the factoring.

5x²- 40x will factor to 5x( __ )

a)

x - 8

b)

8 - x

c)

x² - 8

d)

8 - x²

34.

Complete the factoring.

7x²y⁵ + 56x²y⁴ is factored to 7x²y⁴ ( __ )

a)

y + 8

b)

7y + 8x

c)

y + 8x²

d)

x²y + 8

35.

Find the greatest common factor:

-r⁹s⁵ and -rs⁴

a)

r⁹s⁵

b)

s⁴

c)

rs⁴

d)

r⁹s⁴

36.

Find the greatest common factor of the terms.

12t and 18

a)

6t

b)

36t

c)

6

d)

12

37.

Complete the factoring:

x² - 12x + 32 is factored into (x-8)(___)

a)

x - 4

b)

x + 4

c)

x² + 8

d)

8 - x

38.

Complete the factoring:

x² - 2x - 63 factors to (x - 9) ( ___ )

a)

9 - x

b)

x - 7

c)

x + 7

d)

x²+ 9

39.

Factor Completely:

2r² -17rt + 8t²

a)

Prime

b)

(2r + t)( r - 8t)

c)

(2r + t)(r + 8t)

d)

(2r - t)(r - 8t)

40.

Factor Completely:

x²+ 3x - 28

a)

(x - 7)(x - 4)

b)

(x - 7)(x + 4)

c)

(x + 7)(x - 4)

d)

( x + 7)(x + 4)

41.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

42.

Factor completely.
3x²- 9x -120

a)

3(x - 8)(x + 5)

b)

3(x + 8)(x - 5)

c)

(3x + 8)(x - 5)

d)

(3x - 8)(x + 5)

43.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

44.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

45.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

46.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

47.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

48.

What is the factored form of 5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

Factoring Review

Total questions: 48

Worksheet time: 9hrs 38mins

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