Rewrite rational expressions using inspection, polynomial division, or technology.
Rewrite an improper rational expression as a quotient plus a remainder term
Problem
Rewrite \((x^2~+~3x~+~5)/(x~+~1)\) in quotient-plus-remainder form.
Big Picture
What this problem is really about
Division first gives a reconstruction statement: the dividend equals the divisor times the quotient plus the remainder. Dividing that identity by the divisor produces quotient plus remainder over the original divisor. Keep the remainder even when it is a constant, and confirm that its degree is lower than the divisor’s degree.
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