Question

How do you write a polynomial function given the real zeroes -5,2,-2 and coefficient 1?

Answer 1

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

Explanation:

`(x+5)(x-2)(x+2) = 0` if `x in {-5, 2, -2}`
`color(white)("XXX")`Since for any value of `x` in this set
`color(white)("XXX")`one of the terms will be `=0`

`(x+5)(x-2)(x+2)`
`color(white)("XXX")=(x+5)(x^2-4)`
`color(white)("XXX")=x^2+5x^2-4x-20`

(I assume when the questions says "coefficient 1" it means the coefficient of the highest order term).