Answer
True; See explanation below
Work Step by Step
The problem asks to prove that a factor is a zero of the polynomial
Given $P(x) = 2x^4 + x^3 - 5x^2 + 10x - 4$ and x = 1/2
Substitute x = 1/2 into P(x)
$P(0.5) = 2(0.5^4) + 0.5^3 - 5 (0.5)^2 + 10 (0.5) - 4$
$P(0.5) = 1/8 + 1/8 - 5/4 + 5 - 4 = 0$
Thus x= 1/2 is a zero of the polynomial
