Question

How do you factor `8x^4+x`?

Answer 1

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

Explanation:

List factors of both terms.

`8x^4 = 8*color(orange)(x)*x*x*x`

`x=color(orange)(x)`

The common factors are just one `color(orange)(x)`.
So let's pull out one `x` from the expression.

`color(orange)(x)(8x^3+1)`

We still need to factor `(8x^3+1)`. Take note that `a^3+b^3 = (a+b)(a^2-ab+b^2)`.

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