Factoring Review

GCF

100

Factor:

7x² + 14x

7x(x+2)

200

Factor:

3ab+3a

3a(b+1)

300

Factor:

10x³+20x²+5x 

5x(2x²+4x+1)

400

Factor:

12c⁴+20c⁶+16c⁵

4c⁴(3+5c²+4c)

or

4c⁴(5c²+4c+3)

500

Factor:

24a²b³+36a³b²+12a³b

12a²b(2b²+3ab+a)

Grouping

100

Factor Completely:

a³+2a²+9a+18

(a²+9)(a+2)

200

Factor Completely: 

x³+4x²+8x+32

(x²+8)(x+4)

300

2xy+2x+y²+y

(2x+y)(y+1)

400

Factor completely:

x³+3x²-4x-12

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

500

Factor Completely: 

36xy-24x-9y+6

3(4x-1)(3y-2)

Quadratics

100

Factor Completely: 

x²-8x+12

(x-6)(x-2)

200

Factor Completely: 

y²-2y-24

(y-6)(y+4)

300

Factor Completely:

2x²-9x-5

(2x+1)(x-5)

400

Factor Completely:

6x²-x-1

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

500

Factor Completely:

6x²-34x-40

2(3x-20)(x+1)

Special Cases

100

Factor Completely:

25x²-36

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

200

Factor Completely:

x²+4

Prime

This is not a difference of squares and cannot be factored.

300

x³-8

(x-2)(x²+2x+4)

400

Factor Completely:

4x⁴-64

4(x+2)(x-2)(x²+4)

500

Factor Completely:

8x⁶+125

(2x²+5)(4x⁴-10x²+25)

Miscellaneous

100

What is the first thing you should always do when factoring a polynomial?

Check for a GCF (Greatest Common Factor)

200

What does it mean if a polynomial expression is Prime?

It cannot be factored

300

Factor Completely:

2x²+2x+60

2(x-5)(x+6)

400

Factor Completely:

27x⁹y⁹-8x³y³

x³y³(9x²y²+6xy+4)

500

Factor Completely:

343b²-7b⁴

7b²(7-b)(7+b)