1. 4.3 “Solve x 2 + bx + c by Factoring” Vocabulary to Know: Monomial Binomial Trinomial Roots of a Function Zeros of a Function Use FOIL to multiply the two binomials… (x + 4)(x – 7) Factoring is sort of like reverse FOIL.

2. Examples: Factor the following: 1. x 2 – 9x + 20 2. x 2 – 3x – 18 3.r 2 + 2r – 63 4.x 2 + 14x + 48

3. More Examples: 5.x 2 + 3x – 12 6. m 2 – 17m + 72 7.y 2 – 4y – 60 8.x 2 – x – 42

4. Special Pattern: Difference of Two Squares: **These are binomials only** a 2 – b 2 = (a + b)(a – b) For example…. 1. x 2 – 25 2.x 2 – 100 3.y 2 – 64 4.m 2 – 49

5. Try These: 1. x 2 – 4x – 12 2.m 2 + m + 72 3.k 2 + 2k - 24 4. y 2 – 7y – 60 5.x 2 – 225 6.p 2 – 15p + 50

6. Find the Roots of the Equations: These problems will have an equal sign and may say…Find zeros, roots, solutions…it means the same thing, where the quadratic hits the x-axis. Examples: 1. x 2 – x – 42 = 0 2.f(x) = x 2 -10x + 25 3.y = x 2 – 7x – 30 4. y 2 = 5y

7. Word Problem 1. You are placing a stone border along two sides of a rectangular garden that measures 9 yards by 12 yards. Your budget limits you to only enough stone to cover 72 yards. How wide should the border be?

8. Another Word Problem 2. Julie is making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the frame is 5 square feet. What is the length of the sides of the frame?