FACTORING POLYNOMIALS

Factoring Nobes/PST

100

Factor into two binomials: 3x²+13x+4

(3x+1)(x+4)

200

Factor into two binomials: 6m²-7m+2

(2m-1)(3m-2)

300

Factor into two binomials: 15a²+7ab-2b²

(5a-b)(3a+2b)

400

Factor into two binomials: 4x²+5xy-6y²

(4x-3y)(x+2y)

500

Factor into two binomials: 16x²+72xy+81y²

(4x+9y)²

Factoring Trinomials- harder

100

Factor completely: x⁴+3x²+2

(x²+1)(x²+2)

200

 Factor completely: n⁴+n²-2

(n+1)(n-1)(n²+2)

300

Factor completely: x⁴-10x²+9

(x+1)(x-1)(x+3)(x-3)

400

Factor completely: 54d-16d⁷

2d(3-2d²)(9+6d²+4d⁴)

500

Factor completely: x³²-1

(x¹⁶+1)(x⁸+1)(x⁴+1)(x²+1)(x+1)(x-1)

Factor by Grouping

100

x⁵-x³-x+1

(x+1)(x-1)²(x²+x+1)

200

x²(x+1)-x(x+1)-2(x+1)

(x+1)²(x-2)

300

y²+x²-49-2xy

(y-x+7)(y-x-7)

400

27-3(x-1)²

3(x+2)(4-x)

500

(u-2v)²-4w²

(u-2v+2w)(u-2v-2w)

Factor GCF/DOTS/Soc/Doc

100

30x¹⁰y⁶-42x¹²y⁵-72x⁷y⁷

6x⁷y⁵(5x³y-7x⁵-12y²)

200

x²(a-b)+3x(a-b)-(a-b)

(a-b)(x²+2)

300

81w⁴-v⁴

(9w²+v²)(3w+v)(3w-v)

400

y³+125

(y+5)(y²-5y+25)

500

c³d⁶-216

(cd²-6)(c²d⁴+6cd²+36)

Miscellaneous Factoring

100

m²-9n²+9-6m

(m-3+3m)(m-3-3m)

200

2(m+n)²+(m+n)-3

(a+b-7)(a+b+4)

300

(a+2b)²-(2b+c)²

(a+4b+c)(a-c)

400

(a+b)³-6(a+b)²-7(a+b)

(a+b)(a+b-7)(a+b+1)

500

m⁸-n⁸

(m⁴+n⁴)(m²+n²)(m+n)(m-n)