Math: Factoring: Common Factor

As a math tutor, you notice the importance of this technique.

Factoring means breaking a number or expression into a product.  For instance, we’ll factor 45:

45=9×5

In earlier posts I’ve mentioned prime factorization:

45=3x3x5

Now we’ll look at factorization of polynomials using common factor.
Example: factor -2x6 + 8x5-12x2

Solution: With the common factor method, we look for the expression that divides into all the terms, then write it out front. What remains in the brackets is each term divided by the common factor.

In this case we notice that 2x2 divides into all the terms. Therefore, we “take it out front”. Actually, we take out -2x2 because whenever the lead term is negative, you take out the negative with the common factor. Inside the brackets we write each term divided by -2x2:

-2x2(x4 -4x3+6)

Common factoring doesn’t have to be as complicated as the example above.  Consider the following:

3x – 15 factors to 3(x – 5)

Working with polynomials, factoring is constantly used.  There are at least five factoring techniques, of which common factor is the first.  I’ll discuss the other techniques in future posts:)

 
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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