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MATH / Let P(x) be a cubic polynomial such that P(0)=−3 and P(1)=4. When P(x) is divided by x²+x+1, the remainder is 2x−1. What is the quotient when P(x) is divided by x²+x+1?

Problem

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problem

Let P(x)P(x) be a cubic polynomial such that P(0)=−3P(0) = -3 and P(1)=4.P(1) = 4. When P(x)P(x) is divided by x2+x+1,x^2 + x + 1, the remainder is 2x−1.2x - 1. What is the quotient when P(x)P(x) is divided by x2+x+1x^2 + x + 1?
Plain-text mathematical notation (without MathML)
Let P(x) be a cubic polynomial such that P(0)=−3 and P(1)=4.  When P(x) is divided by x²+x+1, the remainder is 2x−1.  What is the quotient when P(x) is divided by x²+x+1?
Original LaTeX notation
Let $P(x)$ be a cubic polynomial such that $P(0) = -3$ and $P(1) = 4.$  When $P(x)$ is divided by $x^2 + x + 1,$ the remainder is $2x - 1.$  What is the quotient when $P(x)$ is divided by $x^2 + x + 1$?

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
b6ee3464-7602-5f71-bc47-8274cf37705a
task_key
intermediate~5falgebra--test--b6ee3464-7602-5f71-bc47-8274cf37705a
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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