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

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Step 2: Find m, n where m • n = − 48 and m + n = − 13 , herem = + 3 and n = − 16Step 3: Rewrite the trinomial using the two integers from step 2 to break up themiddle term.212x−13x− 4=212x 3x 16x4Step 4: = 3x( 4x + 1)4( 4x1)Step 5: =( 4x1)( 3x4)+ − − Split the middle term− + Factor the GCF from the first two terms andFactor the GCF from the second two terms+ − Factor out the resulting common binomialfactor ( 4x + 1)ANSWER:212x13x4− − =( 4x1)( 3x4)+ − .3 22) Factor 16x − 98x + 12xcompletely:FIRST: check for a COMMON FACTOR among the coefficients or thevariables. In this case the COMMON FACTOR = 2x ; Factoring out2x 8x 2 − 49x+ 6this factor we get: ( )2We will now use the procedure given above to factor8x− 49x+ 6 .We must remember to include the factor ( 2x ) in our final answer.NOTE: a = + 8, b = − 49, and c = + 6Step 1: Find the product: ac = ( + 8)( + 6)= + 48Step 2: Find m, n where m • n = + 48 and m + n = − 49 , herem = − 1 and n = − 48Step 3: Rewrite the trinomial using the two integers from step 2 to break up themiddle term.28x− 49x+ 62= 8x − x − 48x+ 6 Split the middle termStep 4: x( 8x 1) 6( 8x1)= − − − Factor the GCF from the first two terms andFactor the GCF from the second two termsRevised 03/09 2
Step 5: ( 8x1)( x 6)= − − Factor out the resulting common binomialfactor ( 8x − 1)ANSWER:3 216 98 12x x x− + = 2x( 8x 1)( x 6)− − .3) Factor26x19x10+ + completely: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 = + 6, b = + 19, and c = + 10Step 1: Find the product: ac = ( 6)( 10)= 60Step 2: Find m, n where m • n = 60 and m + n = + 19 , herem = + 4 and 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)= + + .4) Factor26x19x10− + completely: ( Compare this to example 3)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 = + 6, b = − 19, and c = + 10Revised 03/09 3
Page 1: HFCC Math Lab Beginning Algebra -19
Page 5 and 6: x x x2= 3 − 12 + − 4 Split the
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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