Question

The remainder when $x^6-3x^5+2x^2+8$ is divided by $x+1$ is:

• A. $24$
• B. $14$
• C. $8$
• D. $18$

Answer 1

Answer: (B)

$14$

According to the Remainder theorem,

When a polynomial $p\left(x\right)$ is divided by $x+a$, then the remainder is $p(-a)$.
Therefore, put $x+1=0$ we get,

$x=-1$

Now Put the $x=-1$ in given polynomial we get,
$p(-1)=(-1{)}^6-3(-1{)}^5+2(-1{)}^2+8=14$

Hence, the remainder is $14$.