Q4 of 47 Page 80

Determine whether (2x + 1) is a factor of 4x3 + 4x2 – x – 1.

Let f(x) = 4x3 + 4x2 – x – 1

By factor Theorem,


2x + 1 = 0 ; x = – 1/2


∴f(– 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 = 0


∴f(– 1/2) = 0


So, (2x + 1) is a factor of f(x).


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