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