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## Answers

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).

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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

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