Factoring ax^2+bx+c, a is not 1 - The Learning Lab at HFCC

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Step 1: Find the product: ac = ( 6)( 10)= 60Step 2: Find m, n where m • n = 60 and m + n = − 19 , herem = − 4, n = − 15Step 3: Rewrite the trinomial using the two integers from step 2 to break up themiddle term.26x− 19x+ 102= 6x − 4x − 15x+ 10 Split the middle termStep 4: 2x( 3x 2) 5( 3x2)= − − − Factor the GCF from the first two terms andStep 5: ( 3x2)( 2x5)Factor the GCF from the second two terms= − − Factor out the resulting common binomialfactor ( 3x − 2)ANSWER:26x19x10− + ( 3x2)( 2x5)= − − .25) Factor 11x+ 4 − 3xcompletely:2Before you start rewrite 11x+ 4 − 3xin descending order − + +23x11x4FIRST: check for a COMMON FACTOR among the coefficients or thevariables. In this case the COMMON FACTOR = − 1 ; Factoring out2−1 3x−11x− 4this factor we get: ( )2We will now use the procedure given above to factor 3x−11x− 4 . Generally it iseasier to factor a trinomial if the leading coefficient a is positiveWe must remember to include the factor ( − 1) in our final answer.NOTE: a = + 3, b = − 11, and c = − 4Step 1: Find the product: ac = ( − 3)( 4)= − 12 andStep 2: Find m, n where m • n = − 12 and m + n = − 11 , herem = − 12 and n = + 1Step 3: Rewrite the trinomial using the two integers from step 2 to break up themiddle term.23x−11x− 4Revised 03/09 4
x x x2= 3 − 12 + − 4 Split the middle termStep 4: 3x( x 4) 1( x 4)= − + − Factor the GCF from the first two terms andStep 5: ( x 4)( 3x1)Factor the GCF from the second two terms= − + Factor out the resulting common binomialfactor ( x − 4)ANSWER:11x4 3x2+ − =2− 3x+ 11x+ 42−1 3x−11x− 4= ( )( 1)( x 4)( 3x1)= − − + .6) Factor2 23x + 7xy − 6ycompletely:FIRST: check for COMMON FACTOR among the coefficients or the variables.In this case the COMMON FACTOR is 1. Factoring 1 out will notsimplify the problem.NOTE: a = + 3, b = + 7, and c = − 6Step 1: Find the product: ac = ( 3)( − 6)= − 18Step 2: Find m, n where m • n = − 18 and m + n = + 7 , herem = + 9 and n = − 2Step 3: Rewrite the trinomial using the two integers from step 2 to break up themiddle term.3x + 7xy − 6y2 22 2= 3x + 9xy − 2xy − 6ySplit the middle termStep 4: 3x( x 3y) 2y ( x 3y)= + − + Factor the GCF from the first two terms andStep 5: ( x 3y)( 3x 2y)Factor the GCF from the second two terms= + − Factor out the resulting common binomialfactor ( x + 3y)ANSWER:3x 7xy 6y+ − ( x 3y)( 3x 2y)2 2= + − .Revised 03/09 5
Page 1 and 2: HFCC Math Lab Beginning Algebra -19
Page 3: Step 5: ( 8x1)( x 6)= − − Facto
Page 7 and 8: Answers with solutions for most pro
Page 9: 15)18x + 39xy + 6y2 22 2( x xy y )=

Factoring ax^2+bx+c, a is not 1 - The Learning Lab at HFCC

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