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MATH / Let P(x) be a monic polynomial of degree 3. Suppose that P(x) has remainder R(x) when it is divided by (x−1)(x−4), and remainder 2R(x) when it is divided by (x−2)(x−3). Given that …

Problem

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problem

Let P(x)P(x) be a monic polynomial of degree 3. Suppose that P(x)P(x) has remainder R(x)R(x) when it is divided by (x−1)(x−4),(x - 1)(x - 4), and remainder 2R(x)2R(x) when it is divided by (x−2)(x−3).(x - 2)(x - 3). Given that P(0)=5,P(0) = 5, find P(5).P(5).
Plain-text mathematical notation (without MathML)
Let P(x) be a monic polynomial of degree 3.  Suppose that P(x) has remainder R(x) when it is divided by (x−1)(x−4), and remainder 2R(x) when it is divided by (x−2)(x−3).  Given that P(0)=5, find P(5).
Original LaTeX notation
Let $P(x)$ be a monic polynomial of degree 3.  Suppose that $P(x)$ has remainder $R(x)$ when it is divided by $(x - 1)(x - 4),$ and remainder $2R(x)$ when it is divided by $(x - 2)(x - 3).$  Given that $P(0) = 5,$ find $P(5).$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
6673c5e1-3df8-530e-8baf-6889e6e658a6
task_key
intermediate~5falgebra--test--6673c5e1-3df8-530e-8baf-6889e6e658a6
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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