Factoring Polynomials

GCF

100

The GCF of the following set of monomials: 7m, 14m

7m

200

The GCF of the following set of monomials: 3xyz, 9rst, 12def

3

300

Factor the following by removing the GCF: 48y²-72y⁵

24y²(2-3y³)

400

Factor the following polynimial: -24x³-60x²

-12x²(2x+5)

500

Combine like terms and factor by pulling out the GCF:

6 − 2y + 5y² − 10y + 3y² − 12

2(4y²-6y-3)

a = 1

100

Complete the following: x² + 7x + 12 = (x + 3)(x + )

(x+3)(x+4)

200

Factor the following: x² + 8x + 12

(x+2)(x+6)

300

Factor the following: a) x² + 18xy + 45y²

(x+15y)(x+3y)

400

Factor the following: 5x² − 20x + 15

5(x-1)(x-3)

500

Factor: x⁴ + 9x² + 20

(x² + 5)(x² + 4)

a is not 1

100

In the following expression 2x² + 5x + 3 we must find to integers that multiply to ____ and add up to ____.

m: 6, a: 5

200

Factor the following expression: 9x²+6x+1

(3x + 1)²

300

Factor the following expression: 8y²+2y−3

(2y − 1)(4y + 3)

400

Factor the following expression: 12z² + 66z + 30

6(2z + 1)(z + 5)

500

The factored form of 3x² + 19x − 14 is (x + a)(bx + c) where a, b, and c are integers. The value of b^c, to the nearest hundredth, is ________

3^-2=0.11

Grouping

100

Factor the following polynomial:

x² + 2x + 6x + 12

(x+2)(x+6)

200

Factor the following polynomial by grouping: 3m² + 9m + 5m + 15

(x+1)(2x+3)

300

Factor the following by grouping: 4x² + 15y² − 12xy² − 5x

(x − 3y²)(4x − 5)

400

x(x - 2) + y(x - 2) is equivalent to...

(x+y)(x-2)

500

The polynomial 2x²+3x+8x+p has a factor of (2x + 3). The value of p is _____.

12

Difference of Squares

100

Factor the following polynomials using a difference of squares: x² − 49

(x+7)(x-7)

200

Factor: m² − n²

(m+n)(m-n)

300

Factor: t²+36z²

Does NOT factor

400

Factor: 48x⁴-3y⁴

3(2x − y)(2x + y)(4x² + y²)

500

What is the factored form of 81m²-4n²  and detrmine the value of the expression when m=5 and n=2.

(9m+2n)(9m-2n) and 2009