Section 6.4: Factoring Polynomials Chapter 6: Polynomials Section 6.4: Factoring Polynomials

Section 6.4: Factoring Polynomials Goals: To factor a polynomial with terms containing common factors; to factor a perfect square trinomial, a difference of squares, and a sum or difference of cubes

Section 6.4: Factoring Polynomials Find the Greatest Common Factor (GCF) If all the terms of a polynomial have a factor(s) in common, you can factor out that greatest common factor

Section 6.4: Factoring Polynomials Example Factor out the GCF 8y2 + 16y5 = 6a4 – 8a2 + 2a = -15x3y + 9x2y7 = -5x2y – x2 + 3x3y5 + 11x7 =

Section 6.4: Factoring Polynomials Factoring a Difference of Perfect Squares If you have a quadratic equation that has the difference of two terms that are both perfect squares, it factors as: A2 – B2 = (A + B)(A – B)

Section 6.4: Factoring Polynomials Example Factor: x2 – 9 = 4x2 – 25 = 9x2 – 16y2 =

Section 6.4: Factoring Polynomials Example Factor: 100x2 – 81y2 = 3x2 – 75 = 20x2 – 5y2 =

Section 6.4: Factoring Polynomials Factoring a Perfect Square Trinomial A perfect square trinomial has two identical binomial factors a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2

Section 6.4: Factoring Polynomials Example Factor y2 + 4y + 4 = x2 – 14x + 49 = a2 + 22ab + 121b2 = 2x2 – 20x + 50 =

Section 6.4: Factoring Polynomials Factoring a Sum or Difference of Two Cubes The sum or difference of two cubes can be factored as the product of a binomial and a trinomial a3 + b3 = (a + b)(a2 – ab + b2) a3 – b3 = (a – b)(a2 + ab + b2)

Section 6.4: Factoring Polynomials Example Factor x3 + 8 27y3 – 125 a3b3 – c3

Section 6.4: Factoring Polynomials Example Factor 64x3 + y3 2w3 – 432

Section 6.4: Factoring Polynomials Homework: Practice Exercises: Pg. 273 #2-42 (even)