Free Printable Solving for x by factoring

1.

Factor x² + 7x + 12

a)

(x + 2)(x + 10)

b)

(x + 3)(x + 4)

c)

(x + 4)(x + 5)

d)

(x + 4)(x + 6)

2.

x²+ 81

a)

Prime

b)

(x - 9) (x + 9)

c)

(x + 9) (x + 9)

d)

(x - 9) (x - 9)

3.

Factor this difference of cubes:
x³ - 343

a)

(x + 7)(x² - 7x + 49)

b)

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

c)

(x - 7)(x² + 7x + 49)

d)

(x + 7)(x + 7)(x + 7)

4.

Find the factors of x²- 81

a)

(x - 9)(x + 9)

b)

(x + 9)(x + 9)

c)

(x - 9)(x - 9)

d)

Prime

5.

Find all zeros for the polynomial
P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

6.

Factor the polynomial.

12x³- 9x² + 4x - 3

a)

(3x² + 1) (4x - 3)

b)

(3x² - 1) (4x + 3)

c)

(4x² + 1) (3x - 3)

d)

(4x² - 1) (3x + 3)

7.

Which is an example of difference of two squares?

a)

( x³- 4)

b)

( x² - 3)

c)

( x² + 4)

d)

( x² - 4)

8.

Factor using Factoring by Grouping:

2n⁴ + 7n³ - 4n - 14

a)

(n - 2)(n - 2)(n - 2)(2n + 7)

b)

(n - 2)³(2n + 7)

c)

(n³ - 2)(2n + 7)

d)

(n + 1)(n - 1)(2n + 7)

9.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

10.

Factor using Factoring like a Quadratic:

k⁴ - 10k² - 39

a)

(k² - 13)(k² + 3)

b)

(k - 13)(k + 3)

c)

(k² + 15)(k² - 3)

d)

(k + 13)(k - 3)

11.

Factor x³ - 1000 using Difference of Cubes

a)

(x + 10)(x² - 10x + 100)

b)

(x - 10)(x² + 10x + 100)

c)

(x - 1)(x² + 1x + 1)

d)

(x - 5)(x² + 5x + 25)

12.

Solve the following polynomial. $0=x^3-3x^2-4x+12$

(select all that apply)

a)

$x=\pm2$

b)

$x=3$

c)

$x=1$

d)

$x=0$

13.

Solve the following polynomial. $x^4+16=8x^2$

(select all that apply)

a)

$x=0$

b)

$x=\pm2$

c)

$x=\pm4$

d)

$x=8$

e)

$x=1$

14.

Find the zeros. $g\left(x\right)=3x^3-15x^2-72x$

(select all that apply)

a)

$x=-3$

b)

$x=8$

c)

$x=-7$

d)

$x=0$

e)

$x=3$

15.

Find the zeros: (select all that apply)

f\left(x\right)=5w^3-125w

a)

$w=5$

b)

$w=-5$

c)

$w=0$

d)

$w=25$

e)

$w=5i$

16.

a)

A

b)

B

c)

C

d)

D

17.

a)

A

b)

B

c)

C

d)

D

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

A

b)

B

c)

C

20.

a)

A

b)

B

c)

C

d)

D

21.

What is the next step in solving after getting the quadratic in factored form?

(x + 2)(x - 3) = 0

a)

Plug in zero for x

b)

Multiply the binomials

c)

FOIL

d)

Set each binomial factor equal to zero

22.

Solve by factoring: x² = 9x - 20

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

23.

Select the solution(s) for the quadratic: $x^2-11x+19=-5$

a)

3

b)

8

c)

-9

d)

-3

24.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

25.

Solve.
n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

26.

Solve the equation by factoring.

a)

$\left\{1,\ -3\right\}$

b)

$\left\{-3,\ -5\right\}$

c)

$\left\{5\right\}$

d)

$\left\{-4,\ 7\right\}$

27.

Solve: x² - 25=0

a)

{5, -5}

b)

{25, -1}

c)

{-25, 1}

d)

{-5}

28.

Solve: x² = 121

a)

60.5

b)

± 11

c)

± 12

d)

11

29.

Solve the equation by factoring.
x² + 13x + 40 = 0

a)

-8, 5

b)

-40, -1

c)

5, 8

d)

-8, -5

30.

x² + 44 = -15x

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

31.

Factor Completely
$6p^2+90p+300$

a)

$6\left(p+5\right)\left(p+10\right)$

b)

$5\left(p-6\right)\left(p-10\right)$

c)

$6\left(p+5\right)\left(p-10\right)$

d)

$\left(p+8\right)\left(p+9\right)$

32.

Factor Completely
$5x^2+20x-105$

a)

$5\left(x-3\right)\left(x+7\right)$

b)

$5\left(x+3\right)\left(x-7\right)$

c)

$5\left(x-3\right)\left(x-7\right)$

d)

Not Factorable

33.

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

a)

$\left(x-3\right)\left(x+1\right)$

b)

$\left(x-7\right)\left(x+4\right)$

c)

$\left(x-3\right)\left(x-1\right)$

d)

$\left(x+3\right)\left(x-1\right)$

34.

Factor Completely
$m^2+11m+10$

a)

$4\left(m-3\right)\left(m+10\right)$

b)

$\left(m+10\right)\left(m-1\right)$

c)

$\left(m+10\right)\left(m+1\right)$

d)

$\left(m-10\right)\left(m+1\right)$

35.

Factor:
x² + 0x - 144

a)

(x + 12)²

b)

(x - 12)(x + 12)

c)

(x - 12)²

d)

12²

36.

$x^2-100=0$

a)

$\left\{25,4\right\}$

b)

$\left\{-50,2\right\}$

c)

$\left\{-10,10\right\}$

d)

$\left\{0,100\right\}$

37.

$3p^2-17p=30-8p$

a)

$\left\{3,5,-2\right\}$

b)

$\left\{2,-5\right\}$

c)

$\left\{-2,5\right\}$

d)

$\left\{-6,15\right\}$

38.

Factor and solve:

z² − 14z + 45 = 0

a)

z = 1, 45

b)

z = −1, 45

c)

z = −5, 9

d)

z = 5, 9

39.

Select the solution(s) for the quadratic: $x^2-11x+19=-5$

a)

3

b)

8

c)

-9

d)

-3

40.

Solve.
n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

41.

What do the "Zeros" represent on a quadratic equation graph?

a)

x-intercepts

b)

y-intercepts

c)

vertex

d)

focus

42.

x²+ 4x - 32 = 0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

d)

x = -2, 16

43.

Solve 3x² - 192 = 0

a)

-32 or 32

b)

No Solution

c)

-8 or 8

d)

-64 or 64

44.

Solve the quadratic equation.

a)

x = -2, 4

b)

x = -8

c)

x = ±8

d)

No real solution

45.

Solve by Factoring Completely: 3x² + 18x +15 = 0 Hint: Factor GCF first.

a)

x=5 x=-1

b)

x=3 x = 1

c)

x= -5 x= - 1

d)

x= -5 x = 1

46.

Solve by factoring: x² = 9x - 20

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

47.

Solve by factoring: 2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

48.

Solve the following polynomial. $0=x^3-3x^2-4x+12$

(select all that apply)

a)

$x=\pm2$

b)

$x=3$

c)

$x=1$

d)

$x=0$

49.

Find the zeros. $g\left(x\right)=3x^3-15x^2-72x$

(select all that apply)

a)

$x=-3$

b)

$x=8$

c)

$x=-7$

d)

$x=0$

e)

$x=3$

Solving for x by factoring

Total questions: 49

Worksheet time: 12hrs 15mins

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