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Algebra Difficulty 4.8 AIME Find the answer
Let Q(x)=x2+2x+3, and suppose that P(x) is a polynomial such that P(Q(x))=x6+6x5+18x4+32x3+35x2+22x+8. Compute P(2).
A number or a short expression. Spacing and $ signs are ignored.
Solution
Note that Q(−1)=2. Therefore, P(2)=P(Q(−1))=1−6+18−32+35−22+8=2.
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