Question

Given: $P\left(x\right)=$ $12x^3-2x^2+18$ and $Q\left(x\right)=2x-12$. Divide $P\left(x\right)$ by $Q\left(x\right)$ and find the remainder.

• A. $2000$
• B. $2340$
• C. $2538$
• D. $2592$

Answer 1

Answer: (C)

$2538$

According to the remainder theorem: When you divide a polynomial $P\left(x\right)$ by $Q\left(x\right)-c$ the remainder $r$ will be $P\left(c\right)$.
So, $P\left(x\right)=12x^3-2x^2+18$ and $Q\left(x\right)=2x-12$
$2x=12$
$x=6$
Therefore, Remainder, $r=$ $P\left(6\right)=12(6{)}^3-2(6{)}^2+18$
$=$ $2592-72+18=2538$