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MATH / Let P₀(x)=x³+313x²−77x−8 . For integers n≥1 , define P_(n)(x)=P_(n−1)(x−n) . What is the coefficient of x in P₂₀(x) ?

Problem

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problem

Let P0(x)=x3+313x2−77x−8P_0(x) = x^3 + 313x^2 - 77x - 8\,. For integers n≥1n \ge 1\,, define Pn(x)=Pn−1(x−n)P_n(x) = P_{n - 1}(x - n)\,. What is the coefficient of xx\, in P20(x)P_{20}(x)\,?
Plain-text mathematical notation (without MathML)
Let P₀(x)=x³+313x²−77x−8 . For integers n≥1 , define P_(n)(x)=P_(n−1)(x−n) . What is the coefficient of x  in P₂₀(x) ?
Original LaTeX notation
Let $P_0(x) = x^3 + 313x^2 - 77x - 8\,$. For integers $n \ge 1\,$, define $P_n(x) = P_{n - 1}(x - n)\,$. What is the coefficient of $x\,$ in $P_{20}(x)\,$?

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
aafd3bf3-21c3-576a-8658-b6f60566ff8c
task_key
intermediate~5falgebra--test--aafd3bf3-21c3-576a-8658-b6f60566ff8c
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import