EDGE Math 8

Using a Combination of Methods

Some factoring problems may require more than one method. As a general rule, you have to first find out if the terms in the polynomial have a common factor. If there is one, factor out the GCF. Then apply the appropriate methods that you have previously learned.

Example 1

Factor $3 x^{4} - 51 x^{2} + 48.$

Solution

3 x^{4} - 51 x^{2} + 48

= 3 (x^{4} - 17 x^{2} + 16)

Factor out the GCF.

= 3 (x^{2} - 1) (x^{2} - 16)

Factor the trinomial by trial and error.

= 3 (x + 1) (x - 1) (x + 4) (x - 4)

Factor a difference of two squares.

Thus,

3 x^{4} - 51 x^{2} + 48

= 3 (x + 1) (x - 1) (x + 4) (x - 4) .