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 \( |R(5)|.\)

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