Free Printable Factoring polynomials

1.

Factor by using the GCF:
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

2.

Factor by using the GCF:

4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

3.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁵)

d)

3x²(80x³-40-60x⁵)

4.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

5.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

6.

Factor:
v² + 3v - 88

a)

(v + 11)(v - 8)

b)

(v + 22)(v - 4)

c)

(v + 8)(v - 11)

d)

(v - 22)(v + 4)

7.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

8.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

9.

Factor the difference of squares:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

10.

Factor the difference of squares:

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Prime

11.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

12.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

13.

Factor:
n²+ 10n + 25

a)

(n + 5)(n - 5)

b)

(n + 25)(n + 1)

c)

(n - 5)²

d)

(n + 5)²

14.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

15.

Factor:
6x² – 19x – 7

a)

(2x +7)(3x – 1)

b)

(1x – 1)(6x+7)

c)

(2x – 7)(3x+1)

d)

(6x – 7)(1x+1)

16.

Factor:

$2x^2+28x+26$

a)

$2\left(x+13\right)\left(x+1\right)$

b)

$2\left(x-1\right)\left(x-13\right)$

c)

$\left(2x-2\right)\left(x+13\right)$

d)

$\left(2x+26\right)\left(x+1\right)$

17.

Factor:

$11z^2+13z+2$

a)

$\left(11z+2\right)\left(z+1\right)$

b)

$\left(11z+1\right)\left(z+2\right)$

c)

$\left(11z-1\right)\left(z-2\right)$

d)

$\left(11z+2\right)\left(11z-1\right)$

18.

What is the first step in factoring the given trinomial?

$3a^2-21a-90$

a)

Write as two binomials

b)

Factor out the greatest common factor (GCF)

c)

Multiply a * c

d)

Write b

19.

Which expression represents 5x²+11x+2 in factored form?

a)

(x+1)(5x+2)

b)

5(x+2)(x+1)

c)

(x+2)(5x-1)

d)

(x-2)(5x-1)

20.

What method should you use to factor the polynomial?

x² - 36

a)

Factor by Grouping

b)

Factor out the GCF

c)

Difference of Squares

d)

Difference of 2 Cubes

21.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Group

22.

The difference of squares says

a)

a² - b² =
(a + b)(a - b)

b)

a² + b² =
(a + b)(a - b)

c)

a² + b² =
(a + b)(a + b)

d)

a² - b² =
(a - b)(a - b)

23.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

24.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Prime

25.

Which of the following is a perfect square trinomial?

a)

x² – 4x – 4

b)

x² – 6x – 9

c)

x² + 6x – 9

d)

x² – 4x + 4

26.

Put into standard form (highest exponent on the left, constant on the right):

(x - 3)²

a)

x² + 3x + 9

b)

x² - 3x - 9

c)

x² + 6x - 9

d)

x² - 6x + 9

27.

Put into standard form (highest exponent on the left, constant on the right):

(x + 6)²

a)

x² + 6x + 12

b)

x² + 6x + 36

c)

x² + 12x + 6

d)

x² + 12x + 36

28.

Factor

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

29.

Is this a perfect square trinomial?
x² + 16x + 64

a)

Yes

b)

No

30.

Is this a perfect square trinomial?
x² + 18x + 9

a)

Yes

b)

No

31.

Is this a perfect square trinomial?
x² + 14x + 49

a)

Yes

b)

No

32.

Factor

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

33.

Is this a perfect square trinomial?
x² + 10x + 100

a)

Yes

b)

No

34.

Is this a perfect square trinomial?
x² + 18x + 9

a)

Yes

b)

No

35.

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)

36.

Factor:
5x² + 17x + 6

a)

(5x + 3)(x + 2)

b)

(5x + 2)(x + 3)

c)

(5x + 1)(x + 6)

d)

(5x + 6)(x + 1)

37.

Factor:
6x² – 19x – 7

a)

(2x +7)(3x – 1)

b)

(1x – 1)(6x+7)

c)

(2x – 7)(3x+1)

d)

(6x – 7)(1x+1)

38.

Factor 81c²- 100.

a)

(c - 10)(c + 10)

b)

(3c - 10)(3c + 10)

c)

(9c + 100)(9c - 100)

d)

(9c - 10)(9c + 10)

Factoring polynomials

Total questions: 38

Worksheet time: 2hrs 21mins

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