Polynomial Dilemma

Algebra Level 4

Let P(x) be a polynomial with deg P $$\ge 3$$ and with real coefficients. Suppose that $${ Q }_{ 1 }(x), { Q }_{ 2 }(x), Q(x)$$ are polynomials and $$R(x)$$ is a degree 2 polynomial such that: $P(x) = { Q }_{ 1 }(x)(x+2)-13 = { Q }_{ 2 }(x)({ x }^{ 2 }-3x-4)-5x-11 = Q(x)(x+2)({ x }^{ 2 }-3x-4)+R(x)$

Find $$|R(5)|.$$

×