Factoring

Leading coefficient is 1

100

x^2-x

x(x-1)

200

p^2 + 11p + 28

(x + 4)(x + 7)

300

(x+4)(x+5)

x^2+9x+20

400

x^4 - x^2 - 72

(x-3)(x+3)(x^2-8)

500

x^4 - 1

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

Leading coefficient not 1

100

-9n^2 - 3n

-3n(3n + 1)

200

5p^2 - 41p + 42

(5p - 6)(p - 7)

300

7b^2 + 67b - 30

(7b - 3)(b + 10)

400

-21x^2 + 81x + 120

-3(7x + 8)(x - 5)

500

5p^2 - 4p - 20

Not Factorable

Cubic

100

4X^3 - 12X^2

4X^2(X - 3)

200

3x^3 - 4x^2 - 3x +4

(3x - 4)(x - 1)(x +1)

300

5s^3 - 6s^2 - 45s + 54

(5s - 6)(s^2 - 9)

400

(x^3 - 64)

(X - 4)(X^2 + 4X + 16)

500

64X^3 - 1

(4X - 1)(16X^2 + 4X + 1)

Random

100

If 4, b, and -(3/4) are zeros of p(x), name the factors of p(x)

(x + 3/4)(x - b)(x - 4)

200

46XY +56X^2 +14Y + 16X

(7x +2)(7y + 8)

300

X^8 - 5X^4 + 4

(X^2 - 2)(X^2 + 2)(X + 1)(X - 1)(X^2 + 1)

400

56XY + 7X^2 - 40Y - 5X

(7X - 5)(8Y + X)

500

245b^2xh + 28bx^2k - 140b^2xk - 49bx^2h

7bx(7h - 4k)(5b - x)

Special Cases

100

16x^2 - 1

(4x - 1)(4x + 1)

200

25x^2 - 36

(5x + 6)(5x - 6)

300

24n^2 - 54

6(2n - 3)(2n + 3)

400

175x^2 - 280x + 112

7(5x - 4)^2

500

500b^2 + 100b^3 + 5b^4

5b^2(10 + b)^2