5.4 Factoring Polynomials 1 Methods 2 Examples 3 Practice Problems
Definition If a polynomial is a product of other polynomials, then each polynomial in the product is a factor Factors that contain polynomials of a positive degree are called nontrivial factors Polynomials than cannot be factored are referred to as prime or irreducible
Greatest Common Factor (GCF) Look for the largest common number and/or variables in each term Divide each term by the common terms
Grouping
Rainbow Method (2nd degree Polynomial)
Simplifying Quotients Factor the numerator Factor the denominator Cancel any like polynomials
Special Cases Difference of two Squares: x2 – y2 = (x + y)(x - y) Factoring Formulas Example Difference of two Squares: x2 – y2 = (x + y)(x - y) 9a2 – 16 =(3a)2 – (4)2 = (3a + 4)(3a – 4) Difference of two Cubes: x3 – y3 = (x - y)(x2 + xy + y2) 8a3 – 27 = (2a)3 – (3)3 = (2a – 3)[(2a)2 + (2a)(3) + (3)2] =(2a – 3)(4a2 + 6a + 9) Sum of two Cubes: x3 + y3 = (x + y)(x2 – xy + y2) 125a3 + 1 = (5a)3 + (1)3 = (5a + 1)[(5a)2 – (5a)(1) + (1)2]
Practice Problems Page 242 Problems 5-11, odd 15-37, odd 46-51