Question

If a remainder of $4$ is obtained when $x^3+2x^2-x-k$ is divided by $x-2$, find the value of $k$.

• A. $4$
• B. $6$
• C. $10$
• D. $12$

Answer 1

Answer: (C)

$10$

Let the quotient be $a{x}^2+bx+c$, we get
$\Rightarrow x^3+2x^2-x-k=(x-2)(a{x}^2+bx+c)+4$

$=a{x}^3+(b-2a)x^2+(c-2b)x+4-2c$

By comparing, we get
$a=1,b=4,c=7$

$\Rightarrow k=14-4=10$