Demonstrate whether each of these statements is true or false for polynomials over a field. a. The
Question:
Demonstrate whether each of these statements is true or false for polynomials over a field.
a. The product of monic polynomials is monic.
b. The product of polynomials of degrees \(m\) and \(n\) has degree \(m+n\).
c. The sum of polynomials of degrees \(m\) and \(n\) has degree max \([m, n]\).
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