Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Add polynomials and write the sum in standard form
Problem
Add the polynomials \((3x^2~+~5x~-~7)\) and \((2x^2~-~x~+~4)\). Give the coefficients of the sum in descending-degree order, including zeros for missing degrees.
Big Picture
What this problem is really about
This addition is really about matching terms that have the same power of x. We’ll keep the quadratic, linear, and constant places separate, add their signed coefficients, and then read the result from highest degree to lowest, using a zero wherever a degree is missing.
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