Question

If the polynomials $x^3+3x^2-m$ and $2x^3-mx+9$ leave the same remainder when they are divided by $(x-2)$, find the value of $m$. Also find the remainder.

• A. 5,15
• B. 3,12
• C. 3,15
• D. 5,12

Answer 1

The correct option is A

5,15

Let $p\left(x\right)=x^3+3x^2-m,q\left(x\right)=2x^3-mx+9$

When $p\left(x\right)$ and $q\left(x\right)$ are divided by $x-2$, we get same remainder $p\left(2\right)=q\left(2\right)$.

$p\left(2\right)=2^3+3(2{)}^2-m$

= $8+12-m$

= $20-m$ .........(1)

Let $q\left(x\right)=2x^3-mx+9$

$q\left(2\right)=2(2{)}^3-m(2)+9$

= $16-2m+9=25-2m$ ............(2)

Given (1) = (2)

$\therefore 20-m=25-2m$

$\Rightarrow 2m-m=25-20\Rightarrow m=5$

Remainder = $p\left(2\right)$

= $20-m=20-5=15$.