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

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7) Factorx+ x − completely:ac = 2 − 10 = − 2022 9 10Step 1: Find the product: ( )( )Step 2: Find m, n where m • n = − 20 and m + n = + 9Checking carefully:None of the m • n = − 20 options will result in m + n = + 9( − 1• + 20 , − 2• + 10 , − 4• + 5, + 1• − 20 , + 2• − 10 , + 4• − 5)Therefore:2The quadratic trinomial 2x+ 9x− 10 cannot be factored usinginteger coefficients.EXERCISES: Factor out the following trinomials completely:1)2)3)4)5)6)7)8)xx22 − 3 − 2xx22 + 5 + 2xx23 −11 − 4xx24 − 16 + 15xx26 − 13 + 6xx22 − 10 + 8210y− 37y+ 7aa25 + 19 − 413) 3r − 22rs + 7s2 23 214) 6x + 2x − 20x15) 18x + 39xy + 6y2 2216) 32y− 4y− 36217) 15a c + 10ac − 25c18) 8x y + 6x y + x y4 2 3 2 2 219) 10 + 11p− 6 p20) 1− y − 56y2229) 2x− 5x+ 710) 6x + 13xy + 2y2 211) 5a − ab − 4b2 212) 6c − 2cd + d2 2221) − 120 + 30w− 50w222) 2t− 7t+ 623) −18a b − 6ab + 4b2 2 324) 2y − 10yz + 3z2 2Revised 03/09 6
Answers with solutions for most problems.:1) m • n = − 4 and m n 322 3 2x−x−22 4 1 2= x − x + x −2x( x 2) 1( x 2)( x 2)( 2x1)= − + −= − ++ = − ( m = − 4, n = + 1)2) m • n = − 4 and m n 3−−22x3x2= − + −22x 4x 1x22x( x 2) 1( x 2)( x 2)( 2x1)= − + −= − ++ = − ( m = − 4, n = + 1)3) m • n = − 12 and m n 11−−23x11x4= x + x − x −23 12 4x( 3x 1) 4( 3x1)( 3x1)( x 4)= + − += + −+ = − ( m = + 1, n = − 12)4) ( 2x− 3)( 2x− 5)5) m • n = 36 and m n 1326x− 13x+ 6= − − +26x 4x 9x62x( 3x 2) 3( 3x2)( 3x2)( 2x3)= − − −= − −6) ( 3x− 4)( x − 2)+ = − ( m = − 4, n = − 9)Revised 03/09 7
Page 1 and 2: HFCC Math Lab Beginning Algebra -19
Page 3 and 4: Step 5: ( 8x1)( x 6)= − − Facto
Page 5: x x x2= 3 − 12 + − 4 Split the
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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