Question

If the polynomial $x^4-6x^3+16x^2-25x+10$ is divided by another polynomial $x^2-2x+k$, the remainder comes out to be $x+a$, then the value of $a$ is

• A. $-1$
• B. $-5$
• C. $1$
• D. $5$

Answer 1

The correct option is B $-5$

Reminder comes out $x+a$

Coefficient of $x$ will be $1$

$-25+4k+16-2k=1$

$-9+2k=1$

$2k=10\Rightarrow k=5$

so, $a=10-k(8-k)$

$=10-5\left(3\right)$

$a=-5$.