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Problem

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problem

Let \[x^8 + 3x^4 - 4 = p_1(x) p_2(x) \dotsm p_k(x),\]where each non-constant polynomial pi(x)p_i(x) is monic with integer coefficients, and cannot be factored further over the integers. Compute p1(1)+p2(1)+…+pk(1).p_1(1) + p_2(1) + \dots + p_k(1).
Plain-text mathematical notation (without MathML)
Let
\[x^8 + 3x^4 - 4 = p_1(x) p_2(x) \dotsm p_k(x),\]where each non-constant polynomial p_(i)(x) is monic with integer coefficients, and cannot be factored further over the integers.  Compute p₁(1)+p₂(1)+…+p_(k)(1).
Original LaTeX notation
Let
\[x^8 + 3x^4 - 4 = p_1(x) p_2(x) \dotsm p_k(x),\]where each non-constant polynomial $p_i(x)$ is monic with integer coefficients, and cannot be factored further over the integers.  Compute $p_1(1) + p_2(1) + \dots + p_k(1).$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
a5a54c86-e292-5e67-96e8-b4cfc74be017
task_key
intermediate~5falgebra--test--a5a54c86-e292-5e67-96e8-b4cfc74be017
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import