Question

How do you determine the binomial factors of `x^3+4x^2-x-4`?

Answer 1

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

Explanation:

It is apparent from the given polynomial `x^3+4x^2-x-4`, that if `x^2` is taken from first two terms, we have `x+4` left out and this is also left out if take out `-1` from remaining two terms.

Hence `x^3+4x^2-x-4`

= `x^2(x+4)-1(x+4)`

= `(x^2-1)(x+4)`

= `(x^2+x-x-1)(x+4)`

= `(x(x+1)-1(x+1))(x+4)`

= `(x-1)(x+1)(x+4)`