Question

How many x intercepts does the polynomial function y=(x-8)(x+3)^2

Answer 1

The answer is 2 x-intercepts

Explanation:

To determine the x-intercepts we set y to zero and solve for x:

y=0

(x-8)(x+3)^2=0

The product of 2 factors is 0 means that one of them must be 0:

x-8=0 ⇒ x=8 →first x-intercept

or (x+3)^2=0 ⇒ x+3=0 ⇒ x=-3 →second x-intercept

Therefore the polynomial function two roots, so it has two x-intercepts x=8 and x=-3

Hope this helps :)