1. Algebra I Notes Section 9.5 (A) Factoring x 2 + bx + c With Leading Coefficient = 1 To factor a quadratic expression means to write it as a product of ________ or _______ linear factors. In this section, we will learn how to factor a quadratic trinomial with a leading coefficient of _____. We know from the FOIL method that: (x + p)(x + q) = x 2 + (p + q)x + (pq)c So to factor x 2 + bx + c, we need to find numbers p and q such that: p + q = b (Linear coefficient) AND pq = c (Constant Term) Example: b c x 2 + 6x + 8 p + q = b pq = c 4 + 2 = 6 (4)(2) = 8 Answer: (x + 4)(x + 2) factors2 1

2. ** P & Q are factors of the Constant Term and they add up to the Coefficient of the Linear Term. Example – Factoring when b and c are positive 1. x 2 + 3x + 21 st :Identify b and cb = ______ c = ______ 2 nd :Find two numbers whose sum is ____ and product is ______ x 2 + 3x + 2 = (x + p)(x + q) = 3 rd : Use FOIL to check Example – Factoring when b is negative and c is positive 2. x 2 – 5x + 61 st :Identify b and cb = ______ c = ______ 2 nd :Find two numbers whose sum is _______ and product is ________ x 2 – 5x + 6 = (x + p)(x + q) p and q must be negative numbers =3 rd : Use FOIL to check 32 3 2 (x + 1)(x + 2) x 2 + 2x + x + 2 x 2 + 3x + 2 -56 6 (x – 2)(x – 3) x 2 - 3x – 2x + 6 x 2 – 5x + 6

3. Example – Factoring when b and c are negative. 3.x 2 – 2x – 8 1 st : Identify b and c b = _____ c = _______ 2 nd : Find two numbers whose sum is ______ and product is ________ x 2 – 2x – 8 = (x + p)(x + q) p and q can’t both be negative numbers = 3 rd : Use FOIL to check Example – Factoring when b is positive and c is negative. 4.x 2 + 7x – 18 1 st : Identify b and c b = _______ c = _______ 2 nd : Find two numbers whose sum is _____ and product is ________ x 2 + 7x – 18 = (x + p)(x + q) p and q can’t both be negative numbers = 3 rd :Use FOIL to check -2-8 -2 -8 (x – 4)(x + 2) x 2 + 2x – 4x – 8 x 2 – 2x - 8 7-18 7 (x + 9)(x – 2) x 2 – 2x + 9x – 18 x 2 + 7x - 18

4. More Examples: Factor the following quadratic trinomials. 5. x 2 – 8x – 9 6. x 2 + 17x – 60 7. 48 + 13x - x 2 8. 72 + 22x + x 2 Sum of factors = -8 Product of factors = -9 (x – 9)(x + 1) Sum of factors = 17 Product of factors = -60 (x + 20)(x – 3) -x 2 + 13x + 48 Sum of factors = -13 Product of factors = -48 -(x – 16)(x + 3) -1(x 2 – 13x – 48) x 2 + 22x + 72 Sum of factors = 22 Product of factors = 72 (x + 18)(x + 4)