Factoring Polynomials

Prime Factorization Form

100

36

=2x18

=2x2x9

=2x2x3x3

=2²x3²

200

225

=3x75

=3x3x25

=3x3x5x5

=3²x5²

300

500

=2x250

=2x2x125

=2x2x5x25

=2x2x5x5x5

=2²x5³

400

625

=5x125

=5x5x25

=5x5x5x5

=5⁴

500

756

=2x378

=2x2x189

=2x2x3x63

=2x2x3x3x21

=2x2x3x3x3x7

=2²x3³x7

Factor

100

6x + 6y

6(x+y)

200

ax+cy+xy+ac

=(ax+xy) + (cy+ac)

=x(a+y) + c(y+a)

=(x+c)(a+y)

300

18r²-6+24r

6(3r²-1+4r)

400

6x³-2x²y+z³

prime

500

cdh³+c²dh+c³d²h²

cdh(h²+c+c²dh)

Difference of Two Squares

100

y²-9

(y+3)(y-3)

200

-64+4x²

=4(-16+x²)

=4(x-4)(x+4)

300

x²-y⁴

(x+y²)(x-y²)

400

81x²-64y²

(9x-8y)(9x+8y)

500

4x²+16y²

4(x²+4y²)

Factoring Trinomial Squares

100

x²-14x+49

(x-7)²

200

a²+8a+16

(a+4)²

300

4x²+4x+1

(2x+1)²

400

9+12x+4x²

(3+2x)²

500

9y²-48y+64

(3y-8)²

Factoringx2+bx+c

100

x²+5x+6

(x+2)(x+3)

200

x²-5x-14

(x-7)(x+2)

300

t²+6rt-27r²

(t-3r)(t+9r)

400

-30+13w+w²

=(w+15)(w-2)

or

=(-2+w)(15+w)

500

16p²-8pq+q²

(4p-q)(4p-q)=(4p-q)²