To check whether 2x+1 is a factor of p(x) or not, find the the remainder when p(x) is divided by 2x+1.
First find the zero of 2x+1.
2x+1 = 0
⇒ x = -1/2
p(x) = 4x³ + 4x² - x - 1
p(-1/2) = 4×(-1/2)³ + 4×(-1/2)² - (-1/2) - 1
= 4×(-1/8) + 4×(1/4) + 1/2 - 1
= -1/2 + 1 + 1/2 - 1
= -1/2 + 1/2 + 1 -1
= 0
Since remainder is 0, 2x+1 is a factor of p(x).
