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 : a2 - b2 = (a + b)(a - b)
b. A DIFFERENCE OF 2 CUBES : a3 - b3 = (a - b)(a2 + ab + b2)
c. A SUM OF 2 CUBES : a3 + b3 = (a + b)(a2 - ab + b2)
d. A SUM OR DIFFERENCE OF 2 HIGHER ODD POWERS : In which the patterns established in 2c. are
extended : a5 + b5 = (a + b)(a4 - a3b + a2b2 - ab3 + b4)
a7 + b7 = (a + b)(a6 - a5b + a4b2 - a3b3 + a2b4 - ab5 + b6) etc.
3) If the polynomial has 3 TERMS, it could be factored as
a. A SQUARE TRINOMIAL : a2 + 2ab + b2 = (a + b)2 or a2 - 2ab + b2 = (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: x2 + 2xy + y2 - 9z2 = (x + y)2 - (3z)2 = (x + y - 3z)(x + y + 3z)
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