Question

What are the zeros of the polynomial function: f(x) = (x – 4)(2x + 1)(x + 7)?

Answer 1

Let f(x)=0

0=(x-4)(2x+1)(x+7)

Are you familiar with the Zero Factor Property? :)
That is what we would use to take the next step.

Set each individual factor equal to zero, and solve them seperately for x. :D

Answer 2

Let:
a = (x-4)
b = (2x + 1)
c = (x + 7)

You can rewrite the function as:

\[f(x) = abc\]

That is, the function's value is determined by multiplying 3 values together. In order for the function to evaluate to zero, you need at least one of its variables to be zero (a, b, or c). So solve each once for zero to get your possible values for x that would cause the function to equal zero.