How do you factor this polynomial expression 4xp4 plus 39xp2 minus 10?

Answer 1

4x4 + 39x2 - 10 : Let y = x2 then the expression can be written as 4y2 + 39y - 10.

This can now be regarded as a quadratic equation. There are several ways of determining the factors of this expression. One method is as follows.

Where the expression is of the standard form ay2 + by + c then take the paired factors of 'a' and the paired factors of 'c', obtain the product for each matched pair and continue until the sum or difference of two matched pairs equals 'b'.

1 4 | 1 10

2 2 | 2 5

The paired factors of 4 and 10 are shown above. It can be seen that :

(4 x 10) - (1 x 1) = 39 is the only combination that produces the required result.

The expression can thus be factored as (4y - 1)(y + 10) or in its original form as :

(4x2 - 1)(x2 +10)