A Brief Review of Factoring Section 6.6 A Brief Review of Factoring

Identifying Name and/or Formula Factoring Organizer Number of Terms in the Polynomial Identifying Name and/or Formula Example A. Any number of terms Common factor The terms have a common factor consisting of a number, a variable, or both 2x2 – 16x = 2x(x – 8) 3x2 + 9y – 12 = 3(x2 + 3y – 4) 4x2y + 2xy2 + xy = xy(4x + 2y + 1) B. Two terms Difference of two squares First and last terms are perfect squares: a2 – b2 = (a + b)(a – b) x2 – y2 = (x + y)(x – y) 16x2 – 1 = (4x + 1)(4x – 1) 25y2 – 9x2 = (5y + 3x)(5y – 3x) C. Three terms Perfect-square trinomial a2 + 2ab + b2 = (a + b)2 a2 2ab + b2 = (a  b)2 x2 – 2xy + y2 = (x – y)2 25x2 – 10x + 1 = (5x – 1)2 16x2 + 24x + 9 = (4x + 3)2

Identifying Name and/or Formula Factoring Organizer Number of Terms in the Polynomial Identifying Name and/or Formula Example D. Three terms Trinomial of the form x2 + bx + c It starts with x2. The constants of the two factors are numbers whose product is c and whose sum is b. x2 – 7x + 12 = (x – 3)(x – 4) x2 + 11x – 26 = (x + 13)(x – 2) x2 – 8x – 20 = (x – 10)(x + 2) E. Three terms Trinomial of the form ax2 + bx + c It starts with ax2, where a is any number but 1. Use trial-and-error or the grouping number method to factor. F. Four terms Factor by grouping Rearrange the order if the first two terms do not have a common factor. wx – 6yz + 2wy – 3xz = wx + 2wy – 3xz – 6yz = w(x + 2y) – 3z(x + 2y) = (x + 2y)(w – 3z)

Example Factor. a. b.

Example Factor.

Example Factor. a. x2 + 4 b. x2 – 10x – 25 There is no way to factor a sum of two squares. The expression cannot be factored it is prime. The factor pairs are (1)(–25) or (–1)(25) or (–5)(5). None of these pairs add up to –10. The expression is prime.