Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Multiply a monomial by a polynomial using the distributive property
Problem
Multiply the monomial \(3x\) by the polynomial \((2x^2~-~5x~+~4)\). Give the coefficients of the product in descending-degree order, including zeros for missing degrees.
Big Picture
What this problem is really about
This product uses the distributive property: the monomial must multiply every term inside the polynomial. For each product, we’ll multiply the numerical coefficients and add the exponents on x, then arrange the terms by degree and include a zero for any missing constant term.
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