Factoring Review

Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms 1. GCF 2 or more Difference of Squares 2 Trinomials 3

Always look for a GCF first! A GCF is something EVERY term has in common Find the GCF

The order does not matter!! Difference of Squares a2 - b2 = (a - b)(a + b) or a2 - b2 = (a + b)(a - b) The order does not matter!! Both terms must be perfect squares Must be subtraction If x2 doesn’t come first, factor out -1

Factor and solve x2 – 25=0 Do you have a GCF? No Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? No Yes Yes x2 – 25 Yes Yes ( )( ) x + 5 x - 5 x=5,-5

Factor and solve 16x2 – 9=0 Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? No 16x2 – 9 Yes Yes Yes Yes (4x )(4x ) + 3 - 3 x= 3/4,-3/4

Factor and solve 36x-49x3 Do you have a GCF? Yes! GCF = x x(36-49x2) Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Yes! GCF = x Yes -x(49x2 – 36) Yes Yes Yes -x(7x )(7x ) - + 6 6 x=0,6/7,-6/7

Factor and solve 50x + 7x2 x(50+7x) x=0, x=-50/7 You cannot factor using difference of squares because there is no subtraction! But you can still look for GCF x(50+7x) x=0, x=-50/7

Factoring Trinomials

Factoring Trinomials Step 1: Make sure everything is on one side of the equation Step 2: Multiply 1st term by last term Step 3: Set up ( ) for factors and divide by 1st term Step 4: Find 2 numbers that multiply to last term and add to middle term Step 5: Simplify fractions, if they do not simplify, bring denominator to the front Step 6: Set equal to 0 and solve

3x2 – 14x + 8 = 0 x = 4, x = 2/3 1) Multiply 3 • (8) = 24; 2) Set up ( ) ( x )( x ) 3 3 What multiplies to 24 and adds to -14? ( x - 12)( x - 2) 3 4) Simplify (if possible). 5) Move denominator(s)in front of “x”. ( x - 4)( 3x - 2) x = 4, x = 2/3

2x2 – 3x – 9 = 0 x = 3, x = -3/2 1) Multiply 2 • (-9) = -18; 2) Set up ( ) ( x )( x ) 2 2 What multiplies to -18 and adds to -3? ( x - 6)( x + 3) 2 4) Simplify (if possible). 5) Move denominator(s)in front of “x”. ( x - 3)( 2x + 3) x = 3, x = -3/2

6x3 + 13x2 = -6x x = -2/3, x = -3/2 1) Rewrite and factor GCF 2) Multiply 6 • (6) = 36; x2 + 13x + 36 3) Set up ( ) ( x )( x ) 6 6 4) What multiplies to 36 and adds to 13? ( x + 4)( x + 9) 6 5) Simplify (if possible). 5) Move denominator(s)in front of “x”. (3x + 2)( 2x + 3) x = -2/3, x = -3/2