Factoring

Binomials

100

x²-16

(x+4)(x-4)

200

25x²-1

(5x-1)(5x+1)

300

x³+8

(x+2)(x²-2x+4)

400

x³-27

(x-3)(x²+3x+9)

500

500x³+4

4(5x+1)(25x²-5x+1)

Trinomials

100

x²-5x+6

(x-2)(x-3)

200

x²+7x+12

(x+3)(x+4)

300

x²+3x-40

(x+8)(x-5)

400

2x²-12x-14

2(x-7)(x+1)

500

6x²-7x-3

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

4-Term Polynomials

100

x³-x²+3x-3

(x²+3)(x-1)

200

3x³+12x²+7x+28

(3x²+7)(x+4)

300

x³+5x²-9x-45

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

400

x⁴+2x³+3x+6

(x³+3)(x+2)

500

x⁵-x³-5x²+5

(x+5)(x-5)(x-1)(x²+x+1)

Challenge Problems

100

Factor completely (over the complex numbers).

x²-6

(x-sqrt(6))(x+(sqrt(6))

200

Factor completely (over the complex numbers).

x²+9

(x-3i)(x+3i)

300

Factor completely (over the complex numbers).

x⁴-13x²+36

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

400

Factor completely (over the complex numbers).

x²-4x+1

(x-2+sqrt(3))(x-2-sqrt(3))

500

Factor completely (over the complex numbers).

x³-x²+2

(x+1)(x-1+i)(x-1-i)