EDGE Math 8

Using a Combination of Methods

Example 2

Factor $x^{4} + 5 x^{3} + 8 x + 40.$

Solution

Note that the terms of the polynomial do not have a common factor other than 1 or $- 1.$ Since there are four terms, you can try factoring by grouping.

x^{4} + 5 x^{3} + 8 x + 40

= (x^{4} + 5 x^{3}) + (8 x + 40)

Group the terms.

= x^{3} (x + 5) + 8 (x + 5)

Factor out the GCF in each group.

= (x + 5) (x^{3} + 8)

Factor out the GCF.

= (x + 5) (x + 2) (x^{2} - 2 x + 4)

Factor a sum of two cubes.

Thus,

x^{4} + 5 x^{3} + 8 x + 40

= (x + 5) (x + 2) (x^{2} - 2 x + 4) .