Question

Check whether the polynomial p(x) = 4x³ + 4x² - x - 1 is a multiple it 2x + 1

Answer 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)