Factor common to all terms: A factor common to all the terms of a
polynomial can be factored out. This is essentially the distributive property in
reverse. For example, all three terms in the polynomial 3 x^3 + 12x^2 – 6x contain
a factor of 3x. Pulling out the common factor yields 3 x(x^2 + 4x – 2).
Difference of squares: You will want to be especially keen at spotting
polynomials in the form of the difference of squares. Whenever you have two
identifiable squares with a minus sign between them, you can factor the
expression like this:
a^2 – b^2 = (a + b)(a – b)For example, 4 x^2 – 9 factors to (2x + 3)(2x – 3).
Squares of binomials: Learn to recognize polynomials that are squares of
binomials:
For example, 4 x^2 + 12x + 9 factors to (2x + 3)^2 , and a^2 – 10a + 25 factors to (a –
5)^2.
CLASSIC FACTORABLES
Factor common to all terms
Difference of squares
Square of a binomial