Question

The polynomial f(x) is written in factored form:

f(x) = (x − 6)(x + 5)(x − 9)

What are the zeros of the polynomial function?

x = 6, x = −5, x = 9
x = 6, x = 5, x = 9
x = −6, x = 5, x = −9
x = −6, x = 6, x = −5, x= 5, x = −9, x = 9

Answer 1

x = 6, x = -5, x = 9

Explanation:

If the polynomial f(x) is written in factored form, f(x) = (x − 6)(x + 5)(x − 9), the zeros of the polynomial function are x = 6, x = -5, x = 9.

x-6=0 x = 6

x+5=0 x = -5

x-9=0 x = 9

Therefore, x = 6, x = -5, x = 9 would be the correct answer.

Answer 2

x = 6, x = -5, x = 9

if f(x)=(x-6)(x+5)(x-9)

Explanation:

The zeros of a polynomial in factored form can be found by setting the polynomial equal to zero and then realizing if a product is zero, then at least one of it's factors is zero.

So we have the zero's are the x's that satisfy

(x-6)(x+5)(x-9)=0.

We just need to solve three equations:

x-6=0

This can be solved by adding 6 on both sides: x=6

x+5=0

This can be solved by subtracting 5 on both sides: x=-5

x-9=0

This can be solved by adding 9 on both sides: x=9

The solutions are in { 6,-5,9 }.