Expand and simplify \((2x^3~+~1)(-4x^2~+~x)\). Then identify the leading term, degree, and leading coefficient.

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simplified polynomial=-8x⁵+2x⁴-4x²+x; leading term=-8x⁵; degree=6; leading coefficient=-8

simplified polynomial=-8x⁵+2x⁴-4x²+x; leading term=-8x⁵; degree=5; leading coefficient=-8

simplified polynomial=-8x⁵+2x⁴-4x²+x; leading term=-8x⁵; degree=4; leading coefficient=-8

simplified polynomial=-8x⁵+2x⁴-4x²+x; leading term=-8x⁵; degree=5; leading coefficient=8

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Curriculum context

Course: Math III
Standard: A-APR.1
Category: Algebra
Domain: Arithmetic with Polynomials and Rational Expressions
Objective: Add, subtract, and multiply polynomials beyond quadratic cases.
Problem type: Simplify a polynomial and identify its degree and leading coefficient