Find the value after Remainder Theorem The expression $4x^3+21x-6$ has the same remainder when divided by $x-a$ or by $x+b$, where $a$ not equals to $b$. Find the value of $a^2+b^2-ab$. I have the answer but I don't know how to work through the question.

Given same remainder, by Polynomial Remainder Theorem we have,
$\displaystyle\ \ \ \ \ \ f(a)=f(-b)$
$\displaystyle\Rightarrow 4a^3+21a-6=-4b^3-21b-6$
$\displaystyle\Rightarrow 4(a^3+b^3)+21(a+b)=0$
$\displaystyle\Rightarrow \frac{(a^3+b^3)}{(a+b)}=a^2+b^2-ab=\frac{-21}{4}$
