Question

Find the remainder when f(x)=2x3-5x2+8x+4 is divided by 2x-1 and use it to determine if 2x-1 is a factor

Answer 1

The remainder of f(x) = 7

Step-by-step explanation:

f(x) = $2x^{3} - 5x^{2} +8x + 4$

Here 2x - 1 is a factor.

We will apply Factor theorem ( states that if (x-a) is a factor of f(x) then f(a) is the remainder)

Putting x = 1/2 in f(x) we will get the remainder.

f(1/2) = 2(1/2)^3 -5(1/2)^2 +8(1/2) +4

=7