SAT Subject Test Mathematics Level 2

Square  of  binomial:

To factor successfully, you have to do more thinking and less cranking. You have to try to figure out
what expressions multiplied will give you the polynomial you’re looking at. Sometimes that means
having a good eye for the test makers’ favorite factorables:

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:

a^2     +   2ab +   b^2     =   (a  +   b)^2

a^2     −   2ab +   b^2     =   (a  −   b)^2

a^2     −   b^2     =   (a  −   b)(a    +   b)

a^2     +   2ab +   b^2     =   (a  +   b)^2

Factor  common  to  all terms

Difference  of  squares

Square  of  a   binomial