# What are the zeros of the polynomial function f(x) = x(2x-1)^2(x-4)^3?

Feb 4, 2016

If a multiplication ends in a zero, then (at least) one of the factors must be zero.

#### Explanation:

So we have three possibilities:
(1)
$x = 0$
(2)
${\left(2 x - 1\right)}^{2} = 0 \to 2 x - 1 = 0 \to x = 1 / 2$
(3)
${\left(x - 4\right)}^{4} = 0 \to x - 4 = 0 \to x = 4$
graph{x(2x-1)^2(x-4)^3 [-14.23, 14.25, -7.12, 7.13]}