Question

How do you factor `4x^5-16x^3+12x` ?

Answer 1

`4x^5-16x^3+12x = 4x(x-1)(x+1)(x-sqrt(3))(x+sqrt(3))`

Explanation:

The difference of squares identity can be written:

`A^2-B^2 = (A-B)(A+B)`

We will use this a couple of times, but first separate out the common factor `4x`...

`4x^5-16x^3+12x = 4x(x^4-4x^2+3)`

`color(white)(4x^5-16x^3+12x) = 4x((x^2)^2-4(x^2)+3)`

`color(white)(4x^5-16x^3+12x) = 4x(x^2-1)(x^2-3)`

`color(white)(4x^5-16x^3+12x) = 4x(x^2-1^2)(x^2-(sqrt(3))^2)`

`color(white)(4x^5-16x^3+12x) = 4x(x-1)(x+1)(x-sqrt(3))(x+sqrt(3))`