Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Write and simplify a polynomial expression for geometric area or volume
Problem
A rectangle has length \(x~+~5\) and width \(x~+~2\). Use the displayed dimensions to write a product model for its area, simplify the expression, and state its degree.
The geometry tells us which operation to use: a rectangle’s area is its length multiplied by its width. We’ll multiply the two displayed polynomial dimensions, combine the linear terms, and then use the greatest exponent in the simplified area expression to identify its degree.
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