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

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