Free Printable Final Factoring Skill Review

1.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

2.

Factor: x² - 20x + 100

a)

(x-10)²

b)

(x+10)²

3.

Factor: x² - 30x + 225

a)

(x + 15)²

b)

(x - 15)²

c)

(x + 25)²

d)

(x - 25)²

4.

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

a)

Yes

b)

No

5.

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

a)

Yes

b)

No

6.

Factor completely

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

7.

What does GCF mean?

a)

green colored frogs

b)

greatest coefficient

c)

greatest common factor

d)

greater common fraction

8.

What is the GCF?

5x^2+20x

a)

5

b)

x

c)

5x

d)

20x

9.

What is the GCF?

$3x^2-2x$

a)

3

b)

3x

c)

x

d)

2

10.

Factor the following

$x^2-25$

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

11.

Fully Factor the Following

$25x^2-81$

a)

(5x-9)²

b)

(5x+9)(5x-9)

c)

25(x-9)²

d)

(9x+5)(9x-5)

12.

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.

13.

Factor completely.

$121x^2-49$

a)

( 11x - 7 ) ²

b)

( 11x - 7 ) ( 11x - 7 )

c)

( 11x + 7 ) ( 11x - 7 )

d)

( 12x + 7 ) ( 12x - 7 )

14.

We can't factor using difference of two square on this binomial:

$49x^2+4y^2$

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 because there is an addition sign.

15.

Factor completely.

$49x^2+16$

a)

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

b)

( 7x + 4 ) ( 7x + 4 )

c)

( 7x - 4 ) ²

d)

does not factor (SUM of squares)

16.

What factoring method should I use?

(x^2–9)

a)

GCF

b)

Grouping

c)

Difference of Squares

d)

Trial and Error

17.

Find the factors of

5m² - 45m + 90

a)

3(m + 1)(m + 8)

b)

5(m - 3)(m - 6)

c)

2(m - 7)(m + 3)

d)

5(m - 5)(m + 3)

18.

Factor completely: $7n^2+9n+2$

a)

Cannot be factored

b)

$\left(7n+2\right)\left(n+1\right)$

c)

$\left(7n+1\right)\left(n+2\right)$

d)

$\left(2n+1\right)\left(5n+2\right)$

19.

Factor completely: $6n^2-7n-5$

a)

$\left(2n+1\right)\left(3n-5\right)$

b)

$\left(3n^2+1\right)\left(2n-5\right)$

c)

Cannot be factored

d)

$\left(2n-1\right)\left(3n+5\right)$

20.

Factor completely: $3n^2-10n+8$

a)

$\left(3n-4\right)\left(n-2\right)$

b)

$\left(3n+4\right)\left(n-2\right)$

c)

$\left(n+4\right)\left(3n+2\right)$

d)

$\left(n+2\right)\left(3n-4\right)$

21.

Factor completely: 9x² - 49

a)

(3x + 7)(3x - 7)

b)

(3x + 7)²

c)

(x - 7)²

d)

(x+7)(x-7)

22.

Factor completely: 5x²-28x+32

a)

(3x-10)(x+6)

b)

(x-8)(5x-4)

c)

(5x-8)(x-4)

d)

(5x-8)(x+7)

23.

Factor completely: $4b^2-24b+20$

a)

$4\left(b-5\right)\left(b-1\right)$

b)

$4\left(b-4\right)\left(b+5\right)$

c)

$2\left(b-5\right)\left(b+4\right)$

d)

$4\left(b-6\right)\left(b+4\right)$

24.

Factor completely: $25h^3+125h^2+100h$

a)

$25h\left(h+4\right)\left(h+1\right)$

b)

$25h\left(h+2\right)\left(h+2\right)$

c)

$25h\left(h+20\right)\left(h+5\right)$

d)

$25\left(h+10\right)\left(h+10\right)$

25.

Factor completely: $10i^3+20i^2-80i$

a)

$10i\left(i+1\right)\left(i-8\right)$

b)

$10\left(i-1\right)\left(i+8\right)$

c)

$10i\left(i-2\right)\left(i+4\right)$

d)

$10\left(i+2\right)\left(i-4\right)$

26.

If the area of a square is $9x^2-42x+49$ , what is the perimeter?

a)

3x-7

b)

12x-28

c)

32-36

d)

12x+28

27.

If the area of a square is $64x^2-144x+81$ , what is the perimeter?

a)

3x-9

b)

8x-9

c)

32x-36

d)

12x-36

28.

The volume of a rectangular prism is $V=9y^3-90y^2+144x$ . What expressions can

represent the dimensions of the prism?

a)

$9x\left(x-4\right)^2$

b)

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

c)

9x, x-8, x-2 units

d)

9x, x-4, x-4 units

Final Factoring Skill Review

Total questions: 28

Worksheet time: 2hrs 20mins

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