MATH121

Flow Chart For Factoring Polynomials

BBEP 2^nd ed. R.4

1.         Take out any COMMON FACTOR  (Monomial, Binomial, etc)

2.         COUNT THE NUMBER OF TERMS

A.        2 TERMS                                            B.  3 TERMS                           C.  4 OR MORE TERMS

Difference of Two Squares                               Perfect Square Trinomial           Group to Diff. Of Squares

Diff. Of Two Cubes                                          General Trinomial                     Group to Common Binomial Factor

Sum of Two Cubes                                           2 term methods             2 term methods

FOLLOW THE FLOW CHART-------THINK METHOD****THINK METHOD---

EXAMPLES:

COMMON  FACTOR:           4x  - 8x + 12x  =  4x(x  -  2x  +  3)

                                                4x (x  +  5)  -  10x (x  +  5)  =  2x(x  +  5)(-5x  +  2x  +  20x  +  50)

DIFF. OF 2 SQUARES          

DIFF OF 2 CUBES                 8x  -  27y  =  (2x  -  3y)(4x  +  6xy  +  9y)

SUM OF 2 CUBES                 8x  +  27y  =  (2x  +  3y)(4x  -  6xy  +  9y)

PERFECT SQUARE TRINOMIAL:                4x  -  20xy  + 25y  =  (2x  -  5y)

GENERAL TRINOMIAL                    10x  +  11xy  -  6y  =  (2x  +  3y)(5x  -  2y)

10x  +  19xy  +  6y  =  (2x  +  3y)(5x  +  2y)

Group to Diff. of Squares          x  +  6x  +  9  -  16y  =  (x  +  3)  -  16y  =  (x  +  3  +  4y)(x  +  3  -  4y)

Group to Common

Binomial Factor                    6ax  -  10by  -  4bx  +  15ay  =   6ax  +  15ay  -  4bx  -  10by  =

                                                                                     3a(2x + 5y)  -  2b(2x + 5y)  =  (2x  +  5y)(3a  –  2b)