Question

How do you find the zeros of the polynomial function with equation `f(x) = 2(x-5)(x+4)^2`?

Answer 1

`x= 5`
`x=-4`

Explanation:

set the equation equal to 0 and solve for each part containing an `x`.
`2(x-5)(x+4)^2 = 0`

`(x-5)= 0`
`(x+4)^2=0` or `(x+4)(x+4)=0` so `x+4=0`

this is a valid approach because its multiplicative and a `0` in any part of the equation will result in `0`.

`x= 5`
`x=-4`

we then plug this into the equation to verify that it works and retain the ones that do. In this equation they both are valid.