Question

How do you factor `h(x)= x^4 + 4x^3 + x^2 - 6x`?

Answer 1

`h(x) = x(x-1)(x+2)(x+3)`

Explanation:

Extract the common factor of `x` from the terms of `x^4+4x^3+x^2-6x`
`color(white)("XXXX")` `=x(x^3+4x^2+x-6)`

Considering the term: `x^3+4x+x-6`
Notice that the coefficients of the first 3 terms sum to the negative of the final constant
`rarr (x-1)` is a factor of this expression.

Using synthetic division (or whatever method you choose):
`color(white)("XXXX")` `= x(x-1)(x^2+5x+6)`

We can use standard AC methods to factor this final term:
`color(white)("XXXX")` `= x(x-1)(x+2)(x+3)`