Factoring ax 2 bx c CA 11 0

Factoring ax 2 + bx + c CA 11. 0

Objective - To factor trinomials in 2 the form ax + bx + c

Factoring Quadratic Trinomials The FORM is the most important thing! ax 2 + bx + c This quadratic trinomial is in STANDARD FORM

IDENTIFYING a, b, and c a is the COEFFICIENT of x 2 b is the COEFFICIENT of x and c is the constant term a, b, and c are NUMBERS (not variables).

Factoring Quadratic Trinomials Step 1: Identify a, b, c Step 2: Create a Factor Cross a·c b Step 3: Solve the Factor Cross Step 4: RE-WRITE the polynomial with FOUR TERMS (separate the middle term into two parts) Step 5: Factor by grouping

Factoring Quadratic Trinomials 60 4 x 2 Factor +16 x + 15 +6 +10 a = 4, b = 16, c = 15 16 ac=(4)(15) = 60 4 x 2 +16 x + 15 4 x 2 + 6 x + 10 x + 15 2 x(2 x + 3) + 5(2 x + 3)(2 x + 5) Check

Factoring Quadratic Trinomials 40 Factor 5 x 2 – 14 x + 8 – 4 – 10 a = 5, b = – 14, c = 8 – 14 ac=(5)(8) = 40 5 x 2 – 14 x + 8 5 x 2 – 4 x – 10 x + 8 x(5 x – 4) + 2(– 5 x + 4) x(5 x – 4) + 2(– 1)(5 x – 4) x(5 x – 4) – 2(5 x – 4)(x – 2) Check

Factoring Quadratic Trinomials – 30 Factor 2 x 2 – 7 x – 15 – 10 +3 a = 2, b = – 7, c = – 15 – 7 ac=(2)(– 15) = – 30 2 x 2 – 7 x – 15 2 x 2 – 10 x + 3 x – 15 2 x(x – 5) + 3(x – 5)(2 x + 3) Check

Factoring Quadratic Trinomials Factor – 2 x 2 – 15 x – 7 Since ALL the terms are negative, we should start by factoring out (– 1) (2 x 2 + 15 x + 7)

Factoring Quadratic Trinomials 14 Factor (– 1) (2 x 2 + 15 x + 7) +14 +1 a = 2, b = 15, c = 7 15 ac=(2)(7) = 14 (– 1) (2 x 2 + 15 x + 7) (– 1) (2 x 2 + 14 x + 1 x + 7) (– 1) [2 x(x + 7) + 1(x + 7)] (– 1)(x + 7)(2 x + 1) Check