THE GOAL IN THIS METHOD IS TO OBTAIN A COMMON POLYNOMIAL

FACTOR WHICH IS THEN FACTORED OUT LEAVING BEHIND A

SECOND POLYNOMIAL.

1) Look for common factors in pairs of terms that when factored out will leave

a common polynomial. (May also be in trios.)

2) Rearrange terms, if necessary, to put those terms with a like factor next to

each other.

3) Use the commutative property of multiplication to arrange each term so

that the greatest common factor is together.

4) Use the distributive property of multiplication over addition (in reverse) for

each pair of terms to factor out the GCF leaving the remaining terms and

operators (+ or -) in parentheses.

5) Use distributive property of multiplication over addition, again, to factor out

the common polynomial factor leaving the remaining terms in parentheses.

EXAMPLE: 2a2 + ab + 2ac + bc

group: (2a2 + ab) + (2ac + bc)

factor out like factor from pairs: a(2a + b) + c(2a + b)

factor out like polynomial to get factors: (2a + b)(a + c)

ALTERNATE ROUTE:

group: (2a2 + 2ac) + (ab + bc)

factor out like factor from pairs: 2a(a + c) + b(a + c)

factor out like polynomial to get factors: (a + c)(2a + b)