Check whether the polynomial p(x) = 4x3 + 4x2 - x - 1 is a multiple it 2x + 1
2x + 1 = 0
= x = -1/2
p(x) = 4x3 + 4x2 -x -1
By factor theorem we know that p(x) will be a multiple of (2x + 1) only when p(-1/2) = 0
p(-1/2) = 4*(-1/2)3 + 4*(-1/2)2 -(-1/2) - 1
p(-1/2) = -4/8 + 4/4 + 1/2 -1
p(-1/2) = -1/2 + 1 + 1/2 -1
p(-1/2) = 0
Therefore p(x) is a multiple of (2x + 1)