Find the remainder when $ p(x) = (x+2)^{101} + (x+3)^{200}$ is divided by $ x^2 +5x + 6 $. Find the remainder when $p(x) = (x+2)^{101} + (x+3)^{200}$ is divided by $ x^2 +5x + 6 $.
HINT.   Set $P(x)=Q(x)(x^2+5x+6)+ax+b$ and choose two suitable values of $x$ to make a simultaneous equation for $a$ and $b$
Set the polynomial x^2 + 5x + 6 to zero then find x by quadratic formula. and put that x in the first polynomial.