Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Simplify a sum or difference of polynomials by combining like terms and writing standard form
Problem
Add the polynomials \((2x^3~+~5x~-~1)\) and \((4x^2~-~x~+~9)\). Give the coefficients of the sum in descending-degree order, including zeros for missing degrees.
Big Picture
What this problem is really about
These polynomials contain different powers, so the key is to line up every degree before adding. We’ll treat a missing power as having coefficient zero, add only coefficients attached to the same power of x, and then read the completed coefficient list from the cubic place down to the constant.
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