Math Problem Statement
Find the values of a and b so that the polynomial 𝒙 𝟒 + 𝒂𝒙 𝟑 − 𝟕𝒙 𝟐 + 𝟖𝒙 + 𝒃 is exactly divisible by (x + 2) as well as (x + 3).
Solution
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Math Problem Analysis
Mathematical Concepts
Polynomial Division
Remainder Theorem
System of Equations
Formulas
Remainder Theorem: P(c) = 0 if (x - c) is a factor of P(x)
Equation for P(-2) and P(-3) based on the given polynomial
Theorems
Remainder Theorem
Factor Theorem
Suitable Grade Level
Grades 10-12
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