Question

How do you factor the expression `15x^3-23x^2+4x`?

Answer 1

`15x^3-23x^2+4x = x(5x-1)(3x-4)`

Explanation:

Separate out the common factor `x`, then use an AC method...

`15x^3-23x^2+4x = x(15x^2-23x+4)`

To factor the quadratic, look for a pair of factors of `AC = 15*4 = 60` with sum `B=23`.

The pair `20, 3` works.

Use this pair to split the middle term and factor by grouping:

`15x^2-23x+4 = 15x^2-20x-3x+4`

`color(white)(15x^2-23x+4) = (15x^2-20x)-(3x-4)`

`color(white)(15x^2-23x+4) = 5x(3x-4)-1(3x-4)`

`color(white)(15x^2-23x+4) = (5x-1)(3x-4)`

Putting it all together:

`15x^3-23x^2+4x = x(5x-1)(3x-4)`