Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Multiply a binomial by a trinomial and simplify by combining like terms
Problem
Multiply the binomial \((x~+~2)\) by the trinomial \((x^2~-~3x~+~4)\). Give the coefficients of the product in descending-degree order, including zeros for missing degrees.
Big Picture
What this problem is really about
The safest way to multiply this binomial and trinomial is to build one complete partial product from each binomial term. We’ll distribute x across all three terms, do the same with two, and then align equal powers so only like terms are combined.
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