Number Theory (Polynomials) Find The Remainder? A polynomial $f(x) = x^{50} + 3x^{49} + 3x + 12$ when divided by $x - a$,  it leaves remainder $3$ & when its quotient is further divided by $x - b$ it leaves remainder $5$, also when $f(x)$ is divided by $x^2 - ( b + a)x + ab$ the remainder is $x + 6$. Find $a$?

So by Remainder theorem, $f(a)=3$ and $f(x)=g(x)(x-a)(x-b)+(x+6)$ for some polynomial $g(x)$. Using the first result in the second, you immediately get …
