Question

Which of the following is a polynomial function in factored form with zeros at -6,-2,and 3?

A. F(x)=(x+6)(x+2)(x-3)
B. F(x)=(x-6)(x-2)(x+3)
C. F(x)=x^3+5x^2-12x-36
D. F(x)=x^3-5x^2-12x+36

Answer 1

The first one is the good one.

Answer 2

A.
`f(x)=(x+6)(x+2)(x-3)`

Explanation:

The zeros or roots of a function are the numbers that when they are entered into the function the output will be 0.

We will evaluate the given numbers (-6,-2,3)to see in wich option all of them wil give us 0 in the output, Let´s start with the first option A) as follows:

`f(-6)=((-6)+6)((-6)+2)((-6)-3)=(0)(-4)(-9)=0`

`f(-2)=((-2)+6)((-2)+2)((-2)-3)=(4)(0)(-5)=0`

`f(3)=((3)+6)((3)+2)((3)-3)=(9)(5)(0)=0`

As we can see this is the correct option in which all of the values give us the output 0 adn we dont need to evaluate the resto of the options (B), C) and D))