Chapter 6 – Polynomials and Polynomial Functions 6.5 – Factoring Cubic Polynomials

6.5 – Factoring Cubic Polynomials Today we will be learning how to: Factor cubic polynomials and solve cubic equations

6.5 – Factoring Cubic Polynomials Special Product Patterns Sum of Two Cubes a3 + b3 + (a + b)(a2 – ab + b2) x3 + 8 = Difference of Two Cubes a3 – b3 = (a – b)(a2 + ab + b2) 27x3 – 1 =

6.5 – Factoring Cubic Polynomials Example 1 27x3 + 216 Factor d3 – 125

6.5 – Factoring Cubic Polynomials Example 2 Factor 10x4 – 10 3m12 + 48m7 – 51m2

6.5 – Factoring Cubic Polynomials Example 3 An open concrete block has four sides and a bottom, but no top. The volume of concrete in the block can be modeled by the expression 2x3 – 8x2 + 10x – 4, where x is the thickness of the concrete. Factor the expression.

6.5 – Factoring Cubic Polynomials HOMEWORK 6.5 Worksheet #1 – 18

6.5 – Factoring Cubic Polynomials Factor by Grouping Some polynomials you can factor by grouping Pairs of terms that have common monomial factors ra + rb + sa + sb = r(a + b) + s(a + b) = (r + s)(a + b)

6.5 – Factoring Cubic Polynomials Example 4 Factor x3 + 4x2 – 36x – 144 4x2(x – 3) – 25(x – 3)

6.5 – Factoring Cubic Polynomials Homework 6.5 Worksheet #19 - 24

6.5 – Factoring Cubic Polynomials Solving Cubic Equations In section 5.3 we found the zeros(roots) of some quadratics by setting them equal to zero, factoring, then solving each for x. We can do the same for some cubic equations

6.5 – Factoring Cubic Polynomials Example 5 Solve 3x3 – 6x = -3x2

6.5 – Factoring Cubic Polynomials Example 6 x3 + 5x2 – 3x = 15

6.5 – Factoring Cubic Polynomials HOMEWORK 6.5 Worksheet #25 – 39 EXTRA CREDIT #31 - 33