Factoring ax2 + bx + c CA 11.0

Objective - To factor trinomials in the form ax2 + bx + c

Factoring Quadratic Trinomials The FORM is the most important thing! ax2 + bx + c This quadratic trinomial is in STANDARD FORM

IDENTIFYING a, b, and c a is the COEFFICIENT of x2 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 Factor 4x2 +16x + 15 a = 4, b = 16, c = 15 ac=(4)(15) = 60 4x2 +16x + 15 4x2 + 6x + 10x + 15 2x(2x + 3) + 5(2x + 3) (2x + 3)(2x + 5) Check  +6 +10 16

Factoring Quadratic Trinomials 40 Factor 5x2 – 14x + 8 a = 5, b = –14, c = 8 ac=(5)(8) = 40 5x2 – 14 x + 8 5x2 – 4x – 10x + 8 x(5x – 4) + 2(–5x + 4) x(5x – 4) + 2(–1)(5x – 4) x(5x – 4) – 2(5x – 4) (5x – 4)(x – 2) Check  –4 –10 –14

Factoring Quadratic Trinomials Factor 2x2 – 7x – 15 a = 2, b = –7, c = – 15 ac=(2)(– 15) = – 30 2x2 –7x – 15 2x2 – 10x + 3x – 15 2x(x – 5) + 3(x – 5) (x – 5)(2x + 3) Check  –30 –10 +3 –7

Factoring Quadratic Trinomials Factor – 2x2 – 15x – 7 Since ALL the terms are negative, we should start by factoring out (– 1) (– 1) (2x2 + 15x + 7)

Factoring Quadratic Trinomials Factor (– 1) (2x2 + 15x + 7) a = 2, b = 15, c = 7 ac=(2)(7) = 14 (– 1) (2x2 + 15x + 7) (– 1) (2x2 + 14x + 1x + 7) (– 1) [2x(x + 7) + 1(x + 7)] (– 1)(x + 7)(2x + 1) Check  14 +14 +1 15