Factoring to Reverse FOIL

You might need to the opposite of the FOIL process on the GED math test. This means that you will begin with a squared variable, a variable, and a constant (just a number). For example:

n² – 10n + 21

You need to find two numbers that when multiplied give you the third term (in this example 21) and when added (or subtracted) give you the second term (in this example -10)

First find out what two numbers when multiplied together give you 21. Just jot down all the possibilities:

21 x 1

-21 x -1

3 x 7

-3 x -7

I think that’s all of them.

Now which of the above two numbers will give you -10 when you add or subtract them?

There is only one possibility, -3 and -7:

-3 -7 = -10

Now just write the two sets of parentheses. Both sets will have the variable for the first term, and the second term will be either of the two numbers we came up with in the step above, either -7 or -3:

(n – 7)(n – 3)

You can check your answer by doing the FOIL process and making sure you come up with what was given to you at the beginning.

n² -10n + 21

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4 comments

  1. isaac says:

    wow thanks i ddnt know it was that easy, im studying for the asvab test, and i kept trying to figure this out. i graduated from highschool six years ago so im trying to refresh… 😀

  2. Chris says:

    Hi, do you have practice tests for math on this site?

  3. Francisco says:

    and for this x² + 5x + 5 ????

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