Factoring Polynomials Review

Quadratic Trinomials

100

x² - 19x + 90

(x-9)(x+10)

200

3x² + 7x + 4

(3x + 4)(x + 1)

300

6x² - 19x - 36

(2x - 9)(3x + 4)

400

2x² - 13x+ 21

(2x - 7)(x - 3)

500

7x⁴ + 21x³ - 14x²

7x²(x² + 3x - 2)

Difference/Sum of Squares

100

x² - 169

(x + 13)(x - 13)

200

4x² - 121

(2x - 11)(2x + 11)

300

16x² + 25

(4x + 5i)(4x - 5i)

400

36x² - 100

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

500

3x²+12y²

2(x + 2yi)(x - 2yi)

Difference/Sum of Cubes

100

x³ - 8

(x - 2)(x² + 2x + 4)

200

x³ + 27

(x + 3)(x²

300

3x³ - 8

Nonfactorable.

400

8x³ - 64

(2x - 4)(4x² +8x + 16)

500

27 + 125x³

(3 + 5x)(9 - 15x + 25x²)

Grouping

100

3x + 7y - 21 - xy

(3 - y)(x - 7)

200

8x³ - 64x² + x - 8

(8x² + 1)(x - 8)

300

12x⁴ + 2x³ - 30x - 5

(2x³ - 5)(6x + 1)

400

8x³ - 64x² + x - 8

(x - 8)(8x² + 1)

500

2x⁴ - x³ - 18x² + 9x

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

Wild Card!

100

Solve by factoring: 2x² - 5x - 12 = 0

x = -3/2, x = 4

200

Find the discriminant: x² - 23x + 11

44

300

Solve 9x² + 16 = 0 by factoring.

4/3i or -4/3i

400

Find 3 numbers, a, b, and c, which give the same answer when added together and multiplied together.

1, 2, and 3

500

Find the next number in the sequence: 1 11 21 1211 111221 312211

13112221