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MASTER PRODUCT METHODMASTER PRODUCT METHOD

© 2004 Fred Rheinhardt

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MASTER PRODUCT METHODMASTER PRODUCT METHOD

GeneralGeneral Form Form

aaxx22 + + bbx + x + ccProblem to beProblem to be factoredfactored

22xx22 + + 55x + x + 33aa = = 22 bb = = 55 cc = = 33

(2 )

Draw a fraction Draw a fraction bar.bar.

Place two sets of Place two sets of parentheses on top parentheses on top of the fraction bar.of the fraction bar.

Write the value of Write the value of aa in three places. in three places.

Write the variable Write the variable in the numerator.in the numerator.( ) ( )

(2 )2

x x

2x2 + 5x + 3

22xx22 + + 55x + x + 33

aa = = 22 bb = = 55 cc = = 33

Multiply Multiply aa times times cc

22 times times 33 equals 6 equals 6

Try to find Try to find mm and and nn such that such thatmm • • nn = 6 and = 6 and mm + + nn = = 55

mm = = 33 and and nn = = 22

( ( 22x + x + ) ( ) ( 22x + ) x + )

22

Write the values of Write the values of mm and and nn in the in the numerator.numerator.

Find the Find the GCFGCF of of each binomial in each binomial in the numerator.the numerator.

Cross out names Cross out names for one. for one.

Write the final Write the final answer.answer.

( x + 1 ) ( 2x + 3 ) 2 2( x + 1 )( 2x + 3 ) 2 ( x + 1 ) ( 2x + 3 )

32

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