Algebra Factoring Quadratic Polynomials

WARMUP Factor:

4-6 Factoring Quadratic Polynomials Recall: Perfect Square Trinomials: a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2 Difference of Squares: a 2 – b 2 = (a + b)(a – b)

4-6 Factoring Quadratic Polynomials AND: Sum and Differences of Cubes a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) a 3 – b 3 = (a – b)(a 2 + ab + b 2 )

4-6 Factoring Quadratic Polynomials a 3 – b 3 = (a – b)(a 2 + ab + b 2 )

4-6 Factoring Quadratic Polynomials a 2 + 2ab + b 2 = (a + b) 2

4-6 Factoring Quadratic Polynomials Polynomials of the form: ax 2 + bx + c ( a  0 ) Are called quadratic (from quadratus in Latin, which means square) or second degree polynomials. ax 2 is the quadratic term bx is the linear term c is the constant term.

4-6 Factoring Quadratic Polynomials A quadratic trinomial is a quadratic polynomial for which a, b, and c are all nonzero integers. The previous examples that we looked at were forms of perfect squares or cubes. Now we’ll factor quadratic trinomials that are not necessarily perfect squares…

4-6 Factoring Quadratic Polynomials If ax 2 + bx + c can be factored into the product (px+q)(rx+s) where p, q, r, s are integers, then: ax 2 + bx + c = (px+q)(rx+s) = prx2 + (ps + qr)x + qs SO: a = prb = ps + qrc = qs

4-6 Factoring Quadratic Polynomials What does all that mean? Let’s look at example 1, p. 188

4-6 Factoring Quadratic Polynomials More examples

4-6 Factoring Quadratic Polynomials How about x 2 + 4x - 3

4-6 Factoring Quadratic Polynomials