Question

How do you find the zeros of `x^3-x^2-10x-8`?

Answer 1

`x=` Either -1 or -2 or +4

Explanation:

`f(x) = x^3-x^2-10x-8`

To find the zeros of this polynomial function we must find all values of x such that `f(x) = 0`

Notice that `f(x)` factorises to `(x+1)(x^2-2x-8)`
Which further factorises to `(x+1)(x+2)(x-4)`

Hence the zeors of `f(x)` occur when `(x+1)(x+2)(x-4) =0`

This occurs when either `(x+1)=0` or `(x+2)=0` or `(x-4)=0`

Therefore the zeros of `f(x)` are either -1 or -2 or +4