Question

What are the zeros of the function y=(x-4)(x² - 12x +36)?

OA. -6, 4, and 6
О в.
O c.
O D. 0, 4, and 6
4 and 6
-6 and -4

Answer 1

To find the zeros, we must completely factor the polynomial:

y=(x-4)(x^2-12x+36) has a quadratic expression in it, which can be factored:

y=(x-4)(x+6)(x+6)

From here, apply the zero product property: if a•b=0, then a=0 or b=0

(0)=(x-4)(x-6)(x-6)

This means, we set each binomial equal to zero, and solve for x:

x-4=0

x=4

x-6=0

x=6

Because the binomial (x+6) accurate twice, it has multiplicity of two, so we only have to write its root once.

The answer is:

x= 4, 6