Question

If $a{x}^3+b{x}^2+cx+d$ is divided by $x-2$, then the remainder is equal

• A. $d$
• B. $a-b+c-d$
• C. $8a+4b+2c+d$
• D. $-8a+4b-2c+d$

Answer 1

Answer: (C)

$8a+4b+2c+d$

Remainder theorem: If $P\left(x\right)$ is divided by $x-a$ then remainder will be $P\left(a\right)$

So, by remainder theorm when $a{x}^3+b{x}^2+cx+d$ is divided by $x-2$, then, remainder $=a(2{)}^3+b(2{)}^2+c\left(2\right)+d=8a+4b+2c+d$