Question

When the polynomial $x^2+3x+1$ is divided by $x+1$, the remainder is

• A. $-1$
• B. $8$
• C. $0$
• D. $-6$

Answer 1

The correct option is A $-1$

Given polynomial is $f\left(x\right)=x^2+3x+1$ and it is divided by $(x+1)$

Remainder theorem states that the remainder of the division of a polynomial $f\left(x\right)$ by a linear polynomial $x-a$ is equal to $f\left(a\right)$

Here, linear polynomial is $x+1$ and $a=-1$

$\therefore f\left(a\right)=f(-1)=(-1{)}^2+3(-1)+1=1-3+1=-1$ is the remainder of the given polynomial $f\left(x\right)$.

Hence, option A is correct.