Question

How do you find the zeros of `x^3+x^2-4x-4`?

Answer 1

This cubic has zeros: `2, -2, -1`

Explanation:

This cubic factors by grouping then using the difference of squares identity:

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

with `a=x` and `b=2` as follows:

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

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

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

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

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

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

Hence zeros:

`2, -2, -1`