FACTORING

GCF Factoring

100

25x^6+15x^4

GCF=5x^4 Solution:5x^4(5x^2+3)

200

3x(y+1)+7w(y+1)

GCF=(y+1) Solution:(y+1)(3x+7w)

300

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

GCF=(x-3) Solution:(x-3)(2x+5)

400

ax+ay+2x+2y

(ax+ay)(2x+2y) GCF=a GCF=2 a(x+y)+2(x+y) Solution:(x+y)(a+2)

500

9x^2+15x+3x+5

(9x^2+15x)(3x+5) GCF=3x GCF=1 3x(3x+5)+1(3x+5) Solution:(3x+5)(3x+1)

Criss-Cross Factoring

100

X^2-x-2

X -2 X 1 X-2x=-x (X+1)(x-2)

200

X^2+7x+10

x 5 x 2 2x+5x=7x (x+5)(x+2)

300

3x^2+16x+5

x 5 3x 1 x+15x=16x (x+5)(3x+1)

400

x^2-8x+16

x -4 x -4 -4x-4x=-8x (x-4)(x-4) (x-4)^2

500

-3x^2-x+4

-x 1 3x 4 -4x+3x=-x (-x+4)(3x+1) -(x+4)(3x+1)

Perfect Squares

100

x²+6x+9

Verify a PST: A=Square root x² B=Square root 9 A=x B=3 Check: 6x=2ab 6x=2(x)(3) 6x=6x Solution:(x+3)²

200

x²-12x+36

Verify PST A=X B=6 Check:-12x=-2(x)(6) -12x=-12x Solution:(x-6)²

300

Factor 25x²-60xy+36y²

A=5x B=6y Check: -60xy=-2(5x)(6y) -60xy=-60xy Solution:(5x-6y)²

400

9x^2-24x+16

A=square root 9x^2 B=square root 16 A=3x B=-4 Check: -24x=2 (3x)(-4) -24x=-24x Solution:(3x-4)^2

500

25x^2-60xy+36y^2

A=5 B=6y Check:-60xy=-2 (5x)(6y) -60xy=-60xy Solution:(5x-6y)^2

Difference of Squares

100

Factor x²-100

A=square root x² B=square root 100 A=x B=10 Solution:(x+10)(x-10)

200

Factor 98x²-72y²

GCF=2 2(49x²-36y²) A=square root 49x² B=square root 72y² A=7x B=6y Solution:2(7x+6y)(7x-6y)

300

4x^2-25

A=s.R 4x^2 B=s.R 25 A=2x B=5 (2x+5)(2x-5)

400

9x^9-y^4

A=3x^3 B=y^2 (3x^3+y^2)(3x^3-y^2)

500

4y^2-36y^9

A=s.r 4y^2 B=s.r 36y^9 A=2y B=6y^3 (2y+6y^3)(2y-6y^3)

Expanding Quadratic Expressions

100

(X+2)(x+5)

X^2+5x+2x+10 X^2+7x+10

200

(2z+1)(3z+4)

6z^2+3z+8z+4 6z^2+11z+4

300

(2x-3)(3x-8)

6x^2-16x-9x+24 6x^2-25x+24

400

-2 (4x-5)(7x-6)

-2 (28x^2-24x-35x+30) -56x^2+48x+70x-60 -56x^2+118x-60

500

2(x+7)(x-3) - (4x+3)(2x-1)

2 (x^2-3x+7x-21) - (8x^2-4x+6x-3) 2 (x^2+4x-21) - (8x^2+2x-3) 2x^2+8x-42-8x^2-2x+3 -6x^2+6x-39