Math 2H Unit 5 Factoring Quadratics

GCF & Trinomials

100

Factor

24ab² + 18ab³

6ab²(4+3b)

200

Factor

x² - 7x + 12

(x - 3)(x - 4)

300

Factor

6x² + 37x + 6

(6x+1)(x+6)

400

Factor

15x² - 27x - 6

3(5x + 1)(x - 2)

GCF & Special Cases

100

Factor

x² - 16x + 64

(x - 8)²

200

Factor

36x² - 9

9(2x+1)(2x-1)

300

Factor

49x⁴ - 64y²

(7x² + 8y)(7x² - 8y)

400

Factor

200x⁴ + 80x³ + 8x³

8x³(5x + 1)²

GCF & Zero Product Property

100

Find the x-intercepts

f(x) = -3(x - 6)(2x + 1)

(6,0) and (-1/2,0)

200

Find the zeros

f(x) = 4x(x + 9)(5x - 10)

(0,0), (-9,0), and (2,0)

300

Find the x-intercepts

f(x) = 3x(2x+3) - (2x+3)

(-3/2,0) and (1/3,0)

400

Solve

8x² - 12x = 0

x=0 and x=3/2

Solving By Factoring

100

Solve by factoring

x² + 3x - 12 = 6

x = 3 and x = -6

200

Solve by factoring

64x² - 4 = 0

(1/4,0) and (-1/4,0)

300

Solve by factoring

5x² - 44x + 120 = -30 + 11x

x = 5 and x = 6

400

A rectangular frame with dimensions of (x + 4) and (x + 6) has an area of 48 square inches. Find both dimensions of the frame.

Dimensions are 6 inches by 8 inches.  (x = 2)

500

A baseball has a height modeled by the equation h(t) = -16t² + 80t, where h represents its height after t seconds since the ball was hit.  After how many seconds will the ball be at a height of 96 feet?

2 and 3 seconds