Question

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

Answer 1

`4a^3+15a^2-4a= color(green)(a(4a-1)(a+4))`

Explanation:

First remove the obvious common factor of `color(red)(a)`
`color(white)("XXX")color(red)(a)(color(blue)(4)a^2+color(orange)(15)acolor(cyan)(-4))`

Use the quadratic formula
or
check for factors of `color(blue)(4)` which when cross multiplied by factors of `color(cyan)(-4)` have a sum of `color(orange)(15)`
to get
`color(white)("XXX")color(red)(a)(color(purple)(4a-1))(color(brown)(a+4))`