Question

What is the sum of the remainders when the polynomial $p\left(x\right)=x^2+3x+1$ is divided by $x-1$ and $x-2$?

• A. 11
• B. 5
• C. 16
• D. 14

Answer 1

The correct option is C 16

From remainder theorem, we know
The remainder when $p\left(x\right)$ is divided by $x-1$, the remainder is $p\left(1\right)$

$\therefore$
$p\left(1\right)=1^2+3\left(1\right)+1=1+3+1=5$

Similarly,
The remainder when $p\left(x\right)$ is divided by $x-2$, the remainder is $p\left(2\right)$
$\therefore$
$p\left(2\right)=2^2+3\left(2\right)+1=4+6+1=11$

$\therefore$ The sum of remainders = 5 + 11 = 16