Question

When we divide $x^2+2x+9$ by $x+1$ we get a remainder of .

• A. 3
• B. 4
• C. 8
• D. 9

Answer 1

The correct option is C 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) = $(-1{)}^2+2\times (-1)+9$ = 8.
So, the remainder = 8.