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MATH / Let P(x) be a nonzero polynomial such that (x−1)P(x+1)=(x+2)P(x) for every real x, and (P(2))²=P(3). Find P((7)/(2)).

Problem

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problem

Let P(x)P(x) be a nonzero polynomial such that (x−1)P(x+1)=(x+2)P(x)(x-1)P(x+1)=(x+2)P(x) for every real xx, and (P(2))2=P(3)\left(P(2)\right)^2 = P(3). Find P(72).P(\tfrac72).
Plain-text mathematical notation (without MathML)
Let P(x) be a nonzero polynomial such that (x−1)P(x+1)=(x+2)P(x) for every real x, and (P(2))²=P(3). Find P((7)/(2)).
Original LaTeX notation
Let $P(x)$ be a nonzero polynomial such that $(x-1)P(x+1)=(x+2)P(x)$ for every real $x$, and $\left(P(2)\right)^2 = P(3)$. Find $P(\tfrac72).$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
af6650f4-e252-58cf-84f2-cac42c878a03
task_key
intermediate~5falgebra--test--af6650f4-e252-58cf-84f2-cac42c878a03
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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