FACTORING

Factoring Trinomials

100

Factor x²+5x+6

(x+3)(x+2)

200

Factor m²-7m+10

(m-5)(m-2)

300

Factor n²+2n- 15

(n-3 )(n+5)

400

Factor x²- 6x +9

(x - 3)(x - 3)

500

Solve: x²  -10x + 21 = 0

x²  -10x + 21 = 0 when factored is equal

(x -7)(x - 3) = 0

using Zero Product Property

x - 7 = 0  or x - 3 = 0

Solutions: x = 7 and x = 3 

Factor Binomials

100

x²-16

(x-4)(x+4)

200

x² - 49

(x+7)(x-7)

300

25x²-9

(5x - 3)( 5x  + 3)

400

Factor  9x²  - 25

(3x-5)(3x+5)

500

Factor 64t²-81

(8t - 9)(8t + 9)

Factor Completely

100

Factor completely: 5x³-20x²-60x

= 5x(x² - 4x-12)

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

200

Factor Completely: 

x⁴ - 81 

x⁴ - 81
=(x²+9)(x² - 9)
= (x²+9)(x+3)(x- 3)

300

When Factored Completely:

12x⁴ + 10x³ - 12x² is equivalent to:

A.    x²(4x + 6)(3x - 2)

B.    2(2x² + 3x)(3x² -2x)

C.    2x²(2x - 3 )(3x  + 2)

D.     2x²(2x  + 3)(3x - 2)

GCF = 2x²

other factors: 6x² + 5x - 6

2x²(6x² + 5x - 6)

factored completely: = 2x²(2x+3)(3x-2)   

Hint: use box method to multiply to check that (2x+3)(3x-2) is equal (6x² + 5x - 6)

400

Factor Completely:

3x²+15x-42

= 3(x²+5x - 14) 

= 3(x + 7)(x - 2) 

500

Factor Completely:

9x³-36x

=9x (x² - 4)

= 9x(x+2)(x-2)

Factor by GCF

100

Factor by GCF 4n³+8n²

4n²(n+2)

200

Factor by GCF 9x² + 15x

3x(3x + 5)

300

Factor by GCF 18a³-6a²

6a²(3a - 1) 

400

Factor by GCF 20x³-10x²

10x²(2x-1)

500

Factor by GCF 12x³-4x²

4x²(3x-1)

Solving Quadratics

100

Solve by factoring: x² + 7 x + 10 = 0

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

x = -5  and x = -2

200

Find the roots of:

x² - 3x - 28 = 0

(x -7 )(x + 4) = 0

x = 7 and x = -4 

are the two Roots

300

x² - 16 = 0

(x + 4)(x - 4) = 0 

x - 4 and x = -4

400

4x²  = 64

divide by 4

x² = 16

square root both sides

x = 4 and x = -4

500

3(x-2)²  = 48

divide by 3 

(x - 2) ² = 16

square root both sides 

x - 2 = 4     and x - 2 = -4

x = 6 and x = -2