Question

If remainder is same when polynomial $p\left(x\right)=x^3+8x^2+17x+ax$ is divided by $(x+2)$ and $(x+1)$. Find the value of $a$.

• A. $0$
• B. $1$
• C. $-1$
• D. $3$

Answer 1

The correct option is A $0$

According to the Remainder theorem, when a polynomial $p\left(x\right)$ is divided by $(x-a)$, then the remainder is the value of $p\left(x\right)$ at $x=a$

Here $p\left(x\right)=x^3+8x^2+17x+ax$

When it is divided by $(x+2)$,

Remainder is $=p(-2)$

$=(-2{)}^3+8(-2{)}^2+17(-2)+a(-2)$

$=-8+32-34-2a$

$=-10-2a$

When it is divided by $(x+1)$,

Remainder is $=p(-1)$

$=(-1{)}^3+8(-1{)}^2+17(-1)+a(-1)$

$=-1+8-17-a$

$=-10-a$

Now, both remainders are equal.

$-10-2a=-10-a$

$-2a+a=0$

$-a=0$

$a=0$