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Juan Set 1 Paper 1 · Q7

Paper 1Algebra

Let P(x)P(x) and Q(x)Q(x) be polynomials with real coefficients such that P(x)+Q(x)P(x)+Q(x) is a second-degree polynomial, and

P(x)⋅Q(x)=−4⋅(x−1)4⋅(x−2)2,P(3)=−16.P(x)\cdot Q(x)=-4\cdot(x-1)^4\cdot(x-2)^2,\qquad P(3)=-16.

What is the value of Q(4)Q(4)?

A12
B24
C36
D48
E54

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