Question

How do you factor `4c^3-2c^2-6c`?

Answer 1

`4c^3-2c^2-6c=c(2c-3)(2c+2)`

Explanation:

Note that all of the terms are divisible by `c`, so we can separate that out as a factor first.

We can then factor the remaining quadratic by completing the square and using the difference of squares identity:

`a^2-b^2 = (a-b)(a+b)`

with `a=(2c-1/2)` and `b=5/2` as follows:

`4c^3-2c^2-6c`

`=c(4c^2-2c-6)`

`=c((2c-1/2)^2-1/4-6)`

`=c((2c-1/2)^2-25/4)`

`=c((2c-1/2)^2-(5/2)^2)`

`=c((2c-1/2)-5/2)((2c-1/2)+5/2)`

`=c(2c-3)(2c+2)`