Question

find the remainder when x³+3x²+3x+1 when divided by x-12

Answer 1

$$\begin{gathered} x-\frac{1}{2}=0 \\ x=\frac{1}{2} \\ Putthisinthegivenpolynomial,p\left(x\right)=x^3+3x^2+3x+1 \\ Remainder=p\left(\frac{1}{2}\right) \\ ={\left(\frac{1}{2}\right)}^3+3{\left(\frac{1}{2}\right)}^2+3\left(\frac{1}{2}\right)+1 \\ =\frac{1}{8}+\frac{3}{4}+\frac{3}{2}+1 \\ =\frac{1+6+12+8}{8} \\ =\frac{27}{8} \end{gathered}$$