Question

When $(x^3-2x+px-q)$ is divided by $(x^2-2x-3)$, the remainder is $(x-6)$. What are the values of $p,q$ respectively.

• A. $-2,-6$
• B. $2,-6$
• C. $-4,12$
• D. $2,6$

Answer 1

The correct option is C $-4,12$

Let $p\left(x\right)=x^3-2x+px-9$

$g\left(x\right)=x^2-2x-3$

$r\left(x\right)=x-6$

According to question

$px=q\left(x\right)+r\left(x\right)$

$g\left(x\right)$

$q\left(x\right)$ be some quotient

$(x^3-2x+px-q)=g\left(x\right)q\left(x\right)+(x-6)$

$x^3-2x+px-q-x+6=q\left(x\right).(x^2-2x-3)$

Now remainder $75$

$\therefore px+4x=0$ $-q+12=0$

$p=-4$ $q=12$