Question

$\text{If}p\left(x\right)=x^2+2x+3\text{is divided by}x–1,\text{then what is the remainder?}$

Answer 1

$\text{By remainder theorem, we know that}\text{if a polynomial f(x) is divided by}\text{(x - a), the remainder obtained is f(a).}$

$\text{From the remainder theorem, when}\text{p(x) is divided by (x – 1), the}\text{remainder is p(1).}$

$p\left(x\right)=x^2+2\left(x\right)+3$
$p\left(1\right)=1^2+2\left(1\right)+3=6$

$\text{Thus the remainder is 6.}$