Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Subtract polynomials and write the difference in standard form
Problem
Subtract the polynomial \((2x^2~-~4x~+~7)\) from the polynomial \((5x^2~+~3x~-~2)\). Give the coefficients of the difference in descending-degree order, including zeros for missing degrees.
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What this problem is really about
The word “from” fixes the order of this subtraction, so we need to subtract the entire second polynomial from the first. We’ll turn that subtraction into addition of the opposite, changing every sign in the second polynomial, then combine matching powers and report the coefficients in descending-degree order.
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