Question

How do you find all zeros of the function `F(x)=2x^3-14x^2-56x-40` given 10 as a zero?

Answer 1

The other two zeros are `-1` and `-2`

Explanation:

Since we are told that `10` is a zero, `(x-10)` must be a factor:

`F(x) = 2x^3-14x^2-56x-40`

`color(white)(F(x)) = (x-10)(2x^2+6x+4)`

`color(white)(F(x)) = 2(x-10)(x^2+3x+2)`

`color(white)(F(x)) = 2(x-10)(x+2)(x+1)`

So the other two zeros are `x=-2` and `x=-1`