Factoring to Solve Quadratic Equations Mrs. Book Liberty Hill Middle School Algebra I

Bellwork Solve and check each equation 6 + 4n = 2 7q + 16 = -3 Factor each expression 2c2 + 29c + 14 3p2 + 32p + 20 -1, -2 and 5/7, (2c + 1)(c + 14), (3p + 2)(p + 10)

Zero-Product Property For every real number a and b, if ab = 0, then a = 0 or b = 0. Example, If (x + 3)(x + 2) = 0, then x +3 = 0 or x + 2 = 0

Using the Zero-Product Property Solve (x + 7)(x – 4) = 0 x + 7 = 0 or x – 4 = 0 Use the Zero-Product Property x = -7 or x = 4 Solve for x

Solve each equation (3y – 5)(y – 2) = 0 (6k + 9)(4k – 11) = 0 (5h + 1)(h + 6) = 0 (5/3, 2); (-3/2, 11/4); (-1/5, -6)

Solving by Factoring Solve x2 + 6x + 8 = 0 (x + 2)(x + 4) = 0 x + 2 = 0 or x + 4 = 0 x = -2 or x = -4

Solve by Factoring x2 – 8x – 48 = 0 12, -4

Solve by Factoring x2 – 12x = -36 12, -4

Real-World Problem Pg. 573 Example 4 & Quick Check

Reminder Factor out the greatest common factor (GCF) If the polynomial has two terms or three terms, look for a difference of two squares, a product of two squares, or a pair of binomial factors.

Reminder If there are four or more terms, group terms and factor to find common binomial factors. As a final check, make sure there are no common factors other than 1.