Question

Find the remainder when $x^3+x^2+x+1$ is divided by $x-\frac{1}{2}$, by using remainder theorem.

Answer 1

Now using reminder theorem,

$D=d\times Q+r$

$(x^3+x^2+x+1)=(x^2+\frac{3}{2}x+\frac{7}{4})(x-\frac{1}{2})+\frac{15}{8}$

Hence, this is the answer.