Factoring Review Factoring Chart This chart will help

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Factoring Review

Factoring Review

Factoring Chart This chart will help you to determine which method of factoring to

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

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

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

Difference of Squares a 2 - b 2 = (a - b)(a + b)

Difference of Squares a 2 - b 2 = (a - b)(a + b) or 2 2 a - b = (a + b)(a - b) The order does not matter!! Both terms must be perfect squares Must be subtraction If x 2 doesn’t come first, factor out -1

Factor x 2 - 25 Do you have a GCF? No Are the Difference

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

Factor 16 x 2 - 9 Do you have a GCF? No Are the

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

Factor 3 36 x-49 x Do you have a GCF? Yes! GCF = x

Factor 3 36 x-49 x Do you have a GCF? Yes! GCF = x x(36 -49 x 2) -x(49 x 2 -36) Are the Difference of Squares steps true? Two terms? Yes 1 st term a perfect square? Yes 2 nd term a perfect square? Yes Subtraction? Yes -x(49 x 2 – 36) -x(7 x+ 6 )(7 x - 6 )

Factor 50 x + 2 7 x You cannot factor using difference of squares

Factor 50 x + 2 7 x You cannot factor using difference of squares because there is no subtraction! But you can still look for GCF x(50+7 x)

Factoring Trinomials

Factoring Trinomials

Factoring Trinomials Step 1: Make sure everything is on one side of the equation

Factoring Trinomials Step 1: Make sure everything is on one side of the equation Step 2: Multiply 1 st term by last term Step 3: Set up ( ) for factors and divide by 1 st 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

3 x 2 – 14 x + 8 = 0 1) Multiply 3 •

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

2 x 2 – 3 x – 9 = 0 1) Multiply 2 •

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

6 x 3 + 13 x 2 = -6 x 1) Rewrite and factor

6 x 3 + 13 x 2 = -6 x 1) Rewrite and factor GCF x(6 x 2 + 13 x + 6) = 0 2) Multiply 6 • (6) = 36; x(x 2 + 13 x + 36) 3) Set up ( ) x( x )( x 6 ) 6 4) What multiplies to 36 and adds x( x + 4)( x + 9) to 13? 6 6 5) Simplify (if possible). 5) Move denominator(s)in front of “x”. x(3 x + 2)( 2 x + 3) x=0, x = -2/3, x = -3/2