Factoring Summary:
When factoring polynomials completely, use the following sequence to organize your thoughts:
1) Look for a COMMON MONOMIAL term.
Then:
2) If the polynomial has 2 TERMS, it could be factored as
a. A DIFFERENCE OF 2 SQUARES : a^{2}  b^{2} = (a + b)(a  b)
b. A DIFFERENCE OF 2 CUBES : a^{3}  b^{3} = (a  b)(a^{2} + ab + b^{2})
c. A SUM OF 2 CUBES : a^{3} + b^{3} = (a + b)(a^{2}  ab + b^{2})
d. A SUM OR DIFFERENCE OF 2 HIGHER ODD POWERS : In which the patterns established in 2c. are
extended : a^{5} + b^{5} = (a + b)(a^{4}  a^{3}b + a^{2}b^{2}  ab^{3} + b^{4})
a^{7} + b^{7} = (a + b)(a^{6}  a^{5}b + a^{4}b^{2}  a^{3}b^{3} + a^{2}b^{4}  ab^{5} + b^{6}) etc.
3) If the polynomial has 3 TERMS, it could be factored as
a. A SQUARE TRINOMIAL : a^{2} + 2ab + b^{2} = (a + b)^{2 }or a^{2}  2ab + b^{2} = (a  b)^{2}
b. A GENERAL TRINOMIAL.
4) If the polynomial has 4 TERMS, it could be factored by
a. GROUPING 2 PAIRS OF TERMS : EX: ab + cb  ad  cd = b(a + c)  d(a + c) = (a + c)(b  d).
b. GROUPING 3 TERMS : EX: x^{2} + 2xy + y^{2}  9z^{2} = (x + y)^{2}  (3z)^{2} = (x + y  3z)(x + y + 3z)
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