Factoring Polynomials Review

Trinomials

100

x²+3x+2

(x+1)(x+2)

200

x²-5x-14

(x-7)(x+2)

300

2x²+6x-56

2(x+7)(x-4)

400

3x²-5x-2

(3x+1)(x-2)

500

10x²-23x-5

(2x-5)(5x+1)

Grouping

100

x²-3x+x-3

(x-3)(x+1)

200

x³-4x²-5x+20

(x²-5)(x-4)

300

ab+3a-4b-12

(a-4)(b+3)

400

3x⁵+33x⁴+9x³+99x²

3x²(x²+3)(x+11)

500

x³+36-6x²-6x

(x²-6)(x-6)

Special Patterns

100

x²-16

(x-4)(x+4)

200

3x²-27

3(x-3)(x+3)

300

x²+12x+36

(x+6)²

400

200x²-162y²

2(10x-9y)(10x+9y)

500

4x²-20x+25

(2x-5)²

Factoring Completely

100

6x⁶-24x⁴

6x⁴(x-2)(x+2)

200

x³+3x²-4x-12

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

300

20x³-14x²-12x

2x(2x+1)(5x-6)

400

x²-3xy-4y²

(x-4y)(x+y)

500

6x²-9x-15

3(2x-5)(x+1)

Solving Polynomial Equations

100

(x+2)(x-5)=0

x=-2 or 5

200

x³-16x=0

x=0, 4, or -4

300

x²=56x-x³

x=0, 7, or -8

400

2x³+23x²=7x³+24x

x=0, 3, 8/5

500

2x²=-9x+18

x=3/2, -6