Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Decide whether an expression is a polynomial in x
Problem
Determine whether \(3x^{2}~-~5x~+~1\) is a polynomial in \(x\). Justify the classification using the requirements for exponents and coefficients.
Big Picture
What this problem is really about
Classifying this expression means checking two separate polynomial requirements. We’ll expose the exponent on every x, including the zero exponent hidden in the constant term, and check that those exponents are nonnegative integers while the coefficients are real numbers; a negative coefficient is not the same as a negative exponent.
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