ong>Answer:

This is an easy step—easy to overlook, unfortunately. If you have a polynomial equation, put all terms on one side and 0 on the other. And whether it’s a factoring problem or an equation to solve, put your polynomial in standard form, from highest to lowest power.

For instance, you cannot solve this equation in this form:

x³ + 6x² + 12x = −8

You must change it to this form:

x³ + 6x² + 12x + 8 = 0

Also make sure you have simplified, by factoring out any COMMON factors. This may include factoring out a −1 so that the highest power has a POSITIVE coefficient. Example: to factor

7 − 6x − 15x² − 2x³

begin by putting it in standard form:

−2x³ − 15x² − 6x + 7

and then factor out the −1

−(2x³ + 15x² + 6x − 7) or (−1)(2x³ + 15x² + 6x − 7)

If you’re solving an equation, you can throw away any common constant factor. But if you’re factoring a polynomial, you must keep the common factor.

Example: To solve 8x² + 16x + 8 = 0, you can divide LEFT and right by the common factor 8. The equation x² + 2x + 1 = 0 has the same roots as the original equation.

Example: To factor 8x² + 16x + 8 , you recognize the common factor of 8 and rewrite the polynomial as 8(x² + 2x + 1), which is identical to the original polynomial. (While it’s true that you will focus your further factoring efforts on x² + 2x + 1, it WOULD be an error to write that the original polynomial equals x² + 2x + 1.)