MATH 121
Flow Chart For Factoring Polynomials
BBEP 2nd 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

4x3 − 8x2+ 12x = 4x(x2 − 2x + 3)

4x2(x + 5) − 10x(x + 5)2 = 2x1(x + 5)1(2x − 5(x + 5)) = 2x(x + 5)(2x − 5x − 25) = 2x(x + 5)(-3x − 25) = -2x(x + 5)(3x + 25)

DIFFERENCE OF 2 SQUARES

16 − x4 = (4 − x2)(4 + x2) = (2 − x)(2 + x)(4 + x2)

64x6 − 25y2 = (8x3 − 5y)(8x3 + 5y)

DIFFERENCE OF 2 CUBES

8x3 − 27y6 = (2x − 3y2)(4x2 + 6xy2 + 9y4)

SUM OF 2 CUBES

8x3 + 27y6 = (2x + 3y2)(4x2 − 6xy2 + 9y4)

PERFECT SQUARE TRINOMIAL

4x2 − 20xy + 25y2 = (2x − 5y)2

GENERAL TRINOMIAL

10x2 + 11xy − 6y2 = (2x + 3y)(5x − 2y)

10x2 + 19xy + 6y2 = (2x + 3y)(5x + 2y)

GROUP TO DIFFERENCE OF SQUARES

x2 + 6x + 9 − 16y6 = (x + 3)2 − 16y6 = (x + 3 + 4y3)(x + 3 − 4y3)

GROUP TO COMMON BINOMIAL FACTOR

6ax − 10by − 4bx + 15ay = 6ax + 15ay − 4bx − 10by
= 3a(2x + 5y) − 2b(2x + 5y)
= (2x + 5y)(3a − 2b)