Question

What is the factored form of 6n^4-24n^3+18n

Answer 1

Let
`f(x) 6n^4-24n^3+18n`

First thing I notice is that all those terms are multiples of 6 and n so we can pull those straight out,

`f(x) = 6n(n^3-4n^2+3)`

Now the trickier part, notice if we let n=1 then
`(n^3-4n^2+3) = 0`. By the factor-remainder theorem this means
`(n-1)` is a factor of
`(n^3-4n^2+3)`.

Now perform polynomial division, dividing
`(n-1)` into
`n^3-4n^2+3`. You are left with the quotient
`(n^2-3n-3)` hence

`f(x)=6n(n-1)(n^2-3n-3)`

Answer 2

Answer: 6n(n^3-4n^2+3) of

Explanation: