1.3 Factoring Polynomials Definition of Factoring Factoring Integers & Monomials Factoring Polynomials

Factors Defined  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 2

Factoring Integers  Integers  Look for a common integer in each term of the polynomial 3

Factoring Monomials  Monomials  Look for a common monomial in each term of the polynomial 4

Polynomials (cont.) Factoring FormulasExample Difference of two Squares: x 2 – y 2 = (x + y)(x - y) 9a 2 – 16 =(3a) 2 – (4) 2 = (3a + 4)(3a – 4) Difference of two Cubes: x 3 – y 3 = (x - y)(x 2 + xy + y 2 ) 8a 3 – 27 = (2a) 3 – (3) 3 = (2a – 3)[(2a) 2 + (2a)(3) + (3) 2 ] =(2a – 3)(4a 2 + 6a + 9) Sum of two Cubes: x 3 + y 3 = (x + y)(x 2 – xy + y 2 ) 125a = (5a) 3 + (1) 3 = (5a + 1)[(5a) 2 – (5a)(1) + (1) 2 ] 5

Practice Problems  Page 44 Problems 45-52,