Question

When we divide $x^2+2x+9$ by $x+1$ we get the remainder as ____ .

• A. 8

Answer 1

The correct option is A 8
According to the remainder theorem, the remainder obtained when a polynomial
P($x$) is divided by ($x-a$) is P(a).

Given, P($x$) = $x^2+2x+9$.
Comparing $(x-a)$ with $(x+1)$,
we get $a=-1.$

Hence,
$P(-1)=(-1{)}^2+2\times (-1)+9=1-2+9=8$

So, the remainder is 8.