Question

How do you factor completely `2x^5 - 7x^3 - 4x`?

Answer 1

`(2x^2 +1)(x+2)(x-2)`

Explanation:

Take out the common factor of `x` first.

`x(2x^4 -7x^2 -4)`

We now have a disguised quadratic, but we treat it the same as a quadratic.

Find factors of 2 and 4 which subtract to make 7.

`"2 +1 "rArr " 1 x 1 = +1"`
`"1 -4 "rArr " 2 x 4 = -8 " rArr -8+1 =-7`

`(2x^2 +1)(x^2 -4)`
`(2x^2 +1)(x+2)(x-2)`