Factoring polynomials

Math Central

Quandaries & Queries

Subject: Factoring polynomials
Name: Joe
Who are you: Student

I am in the eighth grade, and we are learning the equivalent of Algebra 2. I have no ides how to factor (x-2)(x^2-1)-6x-6 You help is most aprreciated. Thank you!

Joe

Hi Joe.

One really useful thing to train yourself to recognize is when you
have a "difference of squares", because it factors. In your question,
part of it is (x² - 1) which is the difference of two perfect squares
(x² is obviously a perfect square and so is 1). Whenever you have a
difference of squares, it factors to the two roots added times the two
roots subtracted. In its general form, this means (a² - b²) = (a +b)(a - b).

For example, (8² - 3²) = 64 - 9 = 55, right? Well so does (8 + 3)(8 - 3).
It even works with negative numbers and fractions:
(0.4² - (-2)²) = 0.16 - 4 = -3.84 and (0.4 + (-2))(0.4 - (-2)) =
(-1.6)(2.4) = -3.84

So if you factor (x² - 1) you will get (x+1)(x-1).

Now if you also factor 6x-6, you will see what to do next.

Hope this helps,
Stephen La Rocque.

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