Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.
Interpret a polynomial-division remainder as a contextual function value
Problem
Revenue \(R(x)\), in dollars, has remainder \(120\) when divided by \(x~-~5\). Interpret the remainder using the Remainder Theorem.
Big Picture
What this problem is really about
The remainder represents the revenue model’s output at the input encoded by the divisor. We’ll match x minus 5 to x minus a, connect the given remainder to R of a, and then interpret that output using dollars. The input identifies where the model is evaluated; it is not added to the monetary output.
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