Question

How do you write a polynomial with zeros -5, 2, -2 and leading coefficient 1?

Answer 1

See explanation.

Explanation:

If `a` is a zero of a polynomial, then it can be divided by `(x-a)`.
Using this law we can write the polynomial as a product of `x-a_i` for all zeros:

`W(x)=(x-(-5))xx(x-2)xx(x-(-2))=`
`(x+5)xx(x-2)xx(x+2)=`
`(x+5)xx(x^2-4)=x^3+5x^2-4x+20`