Free Printable Factoring Practice

1.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

2.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

3.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

4.

Factor:
25x²- 100y²

a)

( 5x - 10y) (5xy + 10y)

b)

( 5x - 10y)²

c)

Prime

d)

( 5x - 50y) (5x + 50y)

5.

3v² - 8v + 5

a)

(3v + 5)(v - 1)

b)

(3v - 5)(v + 1)

c)

(3v - 5)(v - 1)

d)

(3v + 5)(v + 1)

6.

Factor 4x² - 81

a)

(4x - 9)(x + 9)

b)

(2x - 9)(2x + 9)

c)

(2x - 9)(2x - 9)

d)

(4x - 1)(x + 81)

7.

Factor

k^2+7k+10

.

a)

$(k+2)(k-5)$

b)

$(k+2)(k+5)$

c)

$(k+10)(k+4)$

d)

$(k-2)(k-5)$

8.

Factor $k^2-2k-24$

a)

$(k-4)(k+6)$

b)

$(k+4)(k+6)$

c)

$(k+6)(k-1)$

d)

$(k+4)(k-6)$

9.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

10.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

11.

3v² - 8v + 5

a)

(3v + 5)(v - 1)

b)

(3v - 5)(v + 1)

c)

(3v - 5)(v - 1)

d)

(3v + 5)(v + 1)

12.

The factored form of $x^2+3x-4$ is:

a)

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

b)

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

c)

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

13.

The factored form of

y^2-8y-20

is:

a)

$\left(y-10\right)\left(y+2\right)$

b)

$\left(y-2\right)\left(y+10\right)$

c)

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

14.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

15.

3v² - 8v + 5

a)

(3v + 5)(v - 1)

b)

(3v - 5)(v + 1)

c)

(3v - 5)(v - 1)

d)

(3v + 5)(v + 1)

16.

1)Factor: x²+ 6x + 8

a)

(x + 4)(x + 3)

b)

(x + 2)(x + 3)

c)

(x + 4)(x + 2)

d)

(x + 5)(x + 1)

17.

Factor as the product of two binomials.

$x^2-3x-10=$

a)

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

b)

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

c)

$\left(x\cdot2\right)$

d)

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

18.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

19.

Factor:
2x² - 7x + 6

a)

(x -1)(2x - 6)

b)

(x - 3) (2x - 2)

c)

(x - 2) (2x - 3)

d)

(x - 6) (2x - 1)

20.

$x^2+7x+10$

a)

$(x+2)(x+5)$

b)

$(x-2)(x-5)$

c)

$(x+10)(x+4)$

d)

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

21.

$x^2+16x+63$

a)

$(x-7)(x+4)$

b)

$(x+7)(x-9)$

c)

$(x-3)(x-10)$

d)

$(x+7)(x+9)$

22.

$x^2-13x+40$

a)

$(x-5)(x-8)$

b)

$(x+5)(x-8)$

c)

$(x-5)(x+8)$

d)

$(x+6)(x+1)$

23.

$x^2-7x+12$

a)

$(x-3)(x-4)$

b)

$(x+3)(x-4)$

c)

$(x+3)(x+4)$

d)

$(x-2)(x-6)$

24.

$x^2-2x-24$

a)

$(x+4)(x-6)$

b)

$(x+4)(x+6)$

c)

$(x+6)(x-1)$

d)

$(x-4)(x+6)$

25.

$2x^2+7x+6$

a)

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

b)

$(2x+3)(x+2)$

c)

$(x+3)(2x+2)$

d)

prime

26.

$3x^2+4x+1$

a)

$(7x-10)(x-8)$

b)

Not factorable

c)

$(3x+1)(x+1)$

d)

$(3x-1)(x-1)$

27.

Factor $2x^2-4x$

a)

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

b)

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

c)

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

d)

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

28.

Factor $2x^2-4x$

a)

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

b)

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

c)

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

d)

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

29.

Factor completely $-40a+56$

a)

$2\left(-20a+28\right)$

b)

$-2\left(20a-28\right)$

c)

$8\left(-5a+7\right)$

d)

$4\left(10a+14\right)$

30.

Factor completely $4x^5+32x^9$

a)

$4x^5\left(1+8x^4\right)$

b)

$2x^4\left(2+16x^5\right)$

c)

$4x\left(x^5+8x^9\right)$

d)

$2x^2\left(2x^3+16x^7\right)$

31.

Factor completely $24n^4+8n+8$

a)

$8\left(3n^4+n+1\right)$

b)

$4\left(6n^4+2n+2\right)$

c)

$8n\left(3n^3+n+1\right)$

d)

$2\left(12n^4+4n+4\right)$

32.

Factor completely $28v-12+36v^2$

a)

$2\left(14v-6+18v^2\right)$

b)

$2v\left(14v-6+18v^2\right)$

c)

$4v\left(7v-3+9v^2\right)$

d)

$4\left(7v-3+9v^2\right)$

33.

Factor completely $-3m^3-30m^2+18m$

a)

$m\left(-3m^2-30m+18\right)$

b)

$-3m\left(m^2+10m-6\right)$

c)

$3\left(-m^3-10m^2+18m\right)$

d)

$\left(3m^2+6\right)\left(-m-3\right)$

34.

Factor completely $8p^8+20p^2+14p$

a)

$2p^2\left(4p^6+10p+7\right)$

b)

$-2p\left(4p^7+10p+7\right)$

c)

$2p\left(4p^7+10p+7\right)$

d)

$\left(2p^2+7\right)\left(p+1\right)$

35.

Factor completely $4x^2-1$

a)

$\left(2x-1\right)^2$

b)

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

c)

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

d)

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

36.

Factor completely $9r^4-25$

a)

$\left(3r-5\right)^4$

b)

$\left(3r+5\right)^2\left(3r-5\right)^2$

c)

$\left(3r^2+5\right)\left(3r^2-5\right)$

d)

$\left(3r+5\right)\left(3r-5\right)$

37.

Factor completely $x^2-y^2$

a)

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

b)

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

c)

$xy\left(x-y\right)$

d)

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

38.

Factor completely $x^2-16y^2$

a)

$\left(x-4y\right)^2$

b)

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

c)

$16xy\left(x-y\right)$

d)

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

39.

Factor completely $25p^4-36$

a)

$\left(5p^2-6\right)\left(5p^2+6\right)$

b)

$\left(5p^2-6\right)^2$

c)

$\left(5p+6\right)\left(5p-6\right)$

d)

$\left(25p^3-6\right)\left(p+6\right)$

40.

Factor completely $16x^4-9$

a)

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

b)

$\left(4x+3\right)\left(4x-3\right)$

c)

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

d)

$\left(8x^3-3\right)\left(2x+3\right)$

41.

Factor completely $x^2+6x+9$

a)

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

b)

$\left(x+9\right)\left(x+1\right)$

c)

$\left(x+3\right)\left(x-3\right)$

d)

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

42.

Factor completely $9x^2-12x+4$

a)

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

b)

$\left(3x+6\right)\left(x-2\right)$

c)

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

d)

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

43.

Factor completely $9x^4+12x^2+4$

a)

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

b)

$\left(3x^2+6\right)\left(x^2-2\right)$

c)

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

d)

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

44.

Factor completely $x^4+10x^2+21$

a)

$\left(x+3\right)\left(x+7\right)$

b)

$\left(x^2-3\right)\left(x^2+7\right)$

c)

$\left(x^2+3\right)\left(x^2+7\right)$

d)

$\left(x^2+3\right)\left(x^2-7\right)$

45.

Factor completely $x^4-3x^2-18$

a)

$\left(x^2+3\right)\left(x^2-6\right)$

b)

$\left(x^2-3\right)\left(x^2-6\right)$

c)

$\left(x^2+3\right)\left(x^2+6\right)$

d)

$\left(x^2-3\right)\left(x^2+6\right)$

46.

Factor completely $x^4-17x^2-72$

a)

$\left(x^2-9\right)\left(x^2-8\right)$

b)

$\left(x^2+9\right)\left(x^2-8\right)$

c)

$\left(x-3\right)\left(x+3\right)\left(x^2+8\right)$

d)

$\left(x^2-9\right)\left(x^2+8\right)$

47.

Factor completely $x^4+3x^2-54$

a)

$\left(x^2-9\right)\left(x^2-6\right)$

b)

$\left(x^2+9\right)\left(x^2-6\right)$

c)

$\left(x^2-9\right)\left(x^2+6\right)$

d)

$\left(x+3\right)\left(x-3\right)\left(x^2+6\right)$

48.

Factor completely $x^4+4x^2-12$

a)

$\left(x^2-2\right)\left(x^2-6\right)$

b)

$\left(x^2+2\right)\left(x^2+6\right)$

c)

$\left(x^2-6\right)\left(x^2+2\right)$

d)

$\left(x^2+6\right)\left(x^2-2\right)$

49.

Factor completely $x^4+11x^2+24$

a)

$\left(x^2+4\right)\left(x^2+6\right)$

b)

$\left(x^2+2\right)\left(x^2+12\right)$

c)

$\left(x^2+8\right)\left(x^2+3\right)$

d)

$\left(x^2+24\right)\left(x^2+1\right)$

50.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

51.

Factor: x² + 2x – 3

a)

(x - 2)(x + 1)

b)

(x + 1)(x - 3)

c)

(x + 2)(x - 1)

d)

(x - 1)(x + 3)

52.

Factor:

5x³- 7x²

a)

x²(5x - 7)

b)

x(5x²- 7x)

c)

x³(5 - 7x)

d)

Prime

53.

Factor: 25x²- 9

a)

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

b)

(x + 5)(x - 3)

c)

(x - 3)(x + 5)

d)

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

54.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

55.

Factor:
x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

56.

What are the factors of x²+3x-40

a)

(x+10)(x-4)

b)

(x+8)(x-5)

c)

(x+20)(x-2)

d)

(x+1)(x-3)

57.

Factor:
24c⁵ - 12c³

a)

6(4c⁵ - 2c³)

b)

12c³(2c²)

c)

12c³(2c² - 1)

d)

12c³(2c² - 0)

58.

Factor d² - 10d + 25

a)

(d + 5) (d - 5)

b)

(d - 15) (d + 10)

c)

(d + 5) (d - 20)

d)

(d - 5) (d - 5)

59.

Factor: 6x² + 9x

a)

(6x + 1)(x + 3)

b)

(3x + 1)(2x + 3)

c)

3x(2x + 3)

d)

6x(x + 3)

60.

Factor:
6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

61.

Factor:
12x + 9

a)

3(4x + 3)

b)

x(12+9)

c)

3(4x - 3)

d)

not factorable

62.

Find GCF 15n³+25n²

a)

5

b)

15n

c)

5n²

d)

5n

63.

Factor:
5x³-7x²

a)

x²(5x-7)

b)

x(5x²-7x)

c)

x³(5-7x)

d)

Prime

64.

Factor: 49x² - 100

a)

(49x + 100)(x - 1)

b)

(7x - 10)(7x + 10)

c)

(49x - 10)(x + 10)

d)

(7x -10)(7x - 10)

65.

x²+4x-32=0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

66.

a)

A

b)

B

c)

C

d)

D

67.

What are the factors of x²-8x-48

a)

(x-12)(x+4)

b)

(x+12)(x-4)

c)

(x+12)(x+4)

d)

(x-12)(x-4)

68.

Find the factors of x²-81

a)

(x-9)(x+9)

b)

(x+9)(x+9)

c)

(x-9)(x-9)

d)

Can't be factored

69.

Factor:

5x² + 20

a)

5(x + 4)

b)

5x(x + 4)

c)

5(x² + 4)

d)

5x²(x + 4)

70.

Factor by grouping:
$x^3-4x^2-4x+16$

a)

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

b)

$\left(x-4\right)\left(x^2-4\right)$

c)

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

d)

$\left(x-4\right)\left(x-2\right)$

71.

Factor by grouping:
3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the aboe

72.

Factor completely:
2x³+ 5x² - 8x - 20

a)

(x² - 4)(2x + 5)

b)

(2x - 5)(x² + 4)

c)

(2x² - 4)(x + 5)

d)

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

73.

10x⁵y - 40xy³

a)

10xy(x⁴ - 4y²)

b)

cannot be factored

c)

10xy(x² - 2y)(x² + 2y)

d)

(x² - 2y)(x² + 2y)

74.

k³- 27

a)

(k - 3)³

b)

(k - 3)(k² + 3k + 9)

c)

(k + 3)(k² - 3k + 9)

d)

(k - 3)(k² - 3k + 9)

75.

x⁴ - 81

a)

(x² - 9)(x² + 9)

b)

(x - 3)²(x + 3)²

c)

(x - 3)(x + 3)(x² + 9)

d)

(x - 3)⁴

76.

Factor by grouping:
$x^3-4x^2-4x+16$

a)

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

b)

$\left(x-4\right)\left(x^2-4\right)$

c)

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

d)

$\left(x-4\right)\left(x-2\right)$

77.

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)

78.

30x³+15x²-18x-9 hint: GCF then Factor by Grouping

a)

(5x²-3)(6x+1)

b)

(5x²-3)(6x+3)

c)

3(5x²+3)(2x-1)

d)

3(5x²-3)(2x+1)

79.

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)

80.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

81.

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)

82.

Factor. $x^3+x^2-4x-4$

a)

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

b)

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

c)

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

d)

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

e)

Cannot be factored

Factoring Practice

Total questions: 82

Worksheet time: 21hrs 30mins

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