Greatest Common Factor

To factor a polynomial means to rewrite the polynomial as a product of simpler polynomials or of polynomials and monomials. Because polynomials may take many different forms, many different techniques are available for factoring them.

The first method of factoring is called factoring out the GCF (greatest common factor).

Example 1

Factor 5 x + 5 y.

Since each term in this polynomial involves a factor of 5, then 5 is a common factor of the polynomial.

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Example 2

Factor 24 x 3 – 16 x 2 + 8 x.

x is a common factor for all three terms. Also, the numbers 24, –16, and 8 all have the common factors of 2, 4, and 8. The greatest common factor is 8 x.

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