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Algebra Help: How to Factor an Expression

Factors are numbers you multiply together to get another number. When asked to factor an expression, you must find the numbers that multiply together to result in that expression. This article will show how factors work with some simple examples, then move on to some more complicated problems.

Common Factor

If we must factor the expression , we have to find the common factor in our coefficients. The factors of 9 are 1, 3, and 9. The factors of 15 are 1, 3, 5, and 15. Three is the common factor. If we pull three out of the expression, we get . We have factored the expression. Let's look at another example.

Highest Common Factor

Factor the expression . Here we know that 2 is a common factor of 4 and 12. Pulling out the 2 leaves us with 2 and 6, which also have a common factor, so we have not yet completed our factor. We need to find the highest common factor in order to finish our job. The factors of 4 are 1, 2, and 4. The factors of 12 are 1, 2, 3, 4, 6, and 12. We see that 4 is the highest common factor. Factoring out 4 gives us , and we have completed our factor.

Complicated Factoring

Those examples were easy, and we know that you are hungering for a challenge. Sometimes the factors will not be as obvious. Take . The coefficients of 4 and 9 do not have any apparent common factors. You have to ask yourself, which two binomial expressions, when multiplied together, will result in a 4x^2 and -9 with 0x. 4x^2 is (2x^2)^2. And 9 is 3^2. So we have (2x^2)^2-3^2. If you recognize the expression as a difference of squares from your special binomial products, you know that (a+b)(a-b)=a^2-b^2. Plugging in our values, we get . And we have factored the expression.

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