Polynomials and Factoring

Factoring Polynomials

100

Factor: 3x^(2)+3

3(x^(2)+1)

200

Factor: a^(2)b+2ab

ab(a+2)

300

3x^(6)-5x^(3)+2x^(2)

x^(2)(3x^(4)-5x+2)

400

Factor: 9x^(4)-15x^(3)+3x^(2)

3x^(2)(3x^(2)-5x)

500

Factor: 2p^(3)q^(2)+p^(2)q+pq

pq(2p^(2)q+p+1)

Differences of Two Squares

100

Factor: x^(2)-4

(x+2) (x-2)

200

Factor: 4x^(2)-25

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

300

Factor: 36x^(2)-25y^(6)

(6x-5y^(3)) (6x+5y^(3))

400

Factor: 9a^(8)b^(4)-49

(3a^(4)b^(2)+7) (3a^(4)b^(2)-7)

500

Factor: 49x^(4)-9x^(6)

x^(4)(7+3x) (7-3x)

Trinomial Squares

100

Factor: x^(2)+6x+9

(x+3)^(2)

200

Factor: x^(2)-14x+49

(x-7)^(2)

300

Factor: 16a^(2)-40ab+25b^(2)

(4a-5b)^(2)

400

Factor: 27m^(2)+72mn+48n^(2)

3(3m+4n)^(2)

500

Factor: 25x^(2)-70x+49

(5x-7)^(2)

Factoring x^2+bx+c

100

Factor: x^(2)+5x+6

(x+2)(x+3)

200

Factor: x^(2)-8x+12

(x-2)(x-6)

300

Factor: a^(2)+7ab+10b^(2)

(a+2b)(a+5b)

400

Factor: x^(2)-8x-20

(x+2) (x-10)

500

Factor: a^(2)+ab-6b^(2)

(a-2b)(a+3b)

Factoring by Grouping

100

Factor: 6x^(3)-9x^(2)+4x-6

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

200

Factor: x^(3)+x^(2)+x+1

(x+1)(x^(2)+1)

300

Factor: x^(3)+2x^(2)-x-2

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

400

Factor: x^(2)y^(2)+ay^(2)+ab+bx^(2)

(x^(2)+a)(y^(2)+b)

500

Factor: x^(3)+x^(2)+2x-2

(x^(2)+2)+(x-1)