Question

Check:2x+1 is a factor of p(x)=4x³+4x²-x-1.

Answer 1

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).

Answer 2

Zero of 2x+1 = -1/2
p(-1/2)= 4×(-1/2)³+4×(-1/2)²-(-1/2)-1
=4×-1/8+4/4+1/2-1
=-1/2+1+1/2-1
=0
therefore, 2x+1 is a factor of 4x³+4x²-x-1