Question

Which of the following is a polynomial function in standard form with zeros at –6, 2, and 5?

f(x) = x^3 – x^2 – 32x + 60


f(x) = x^3 + x^2 – 32x – 60


f(x) = (x – 6)(x + 2)(x + 5)


f(x) = (x + 6)(x – 2)(x – 5)

Answer 1

in standard form you have to expand it, get rid of the parenthesis.
to start with, you have (x+6)(x-2)(x-5)
to expand it, (x+6)(x^2-7x+10)=x^3-x^2-32x+60

Answer 2

`f(x)= (x+6)(x-2)(x-5)`

Explanation:

zeros at –6, 2, and 5

If 'a', 'b' are the zeros of a polynomial , then function is

f(x)=(x-a)(x-b)

We are given with zeros -6, 2 and 5

Write all the zeros with x inside the parenthesis to get f(x). Change the sign because we multiply by negative inside the parenthesis

`f(x)= (x-(-6))(x-2)(x-5)`

`f(x)= (x+6)(x-2)(x-5)`