Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Find the degree and leading term of a polynomial expression
Problem
Simplify \((3x^{2}~+~1)~+~(5x^{4}~-~x)\). Give the simplified polynomial, its leading term, and its degree.
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What this problem is really about
This problem asks us to simplify first and then interpret standard form. We’ll combine or reorder terms from greatest exponent to least, find the first nonzero term in that order, and use its full term as the leading term and its exponent—not its coefficient—as the degree.
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