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2 cards from this section. Quick, good the night before a test.
Define a polynomial of degree 2 over a ring.
Consider the highest power term.
What does closure property mean in the context of polynomials over a ring?
Think about the operations performed.
What is the degree of the polynomial P(x) = 5x^3 + 4x + 2?
Look at the power of x terms.
True or False: The sum of two polynomials of degrees 2 and 3 will always yield a polynomial of degree 3.
Think about which degree dominates.
Create two polynomials over a ring defined by integers modulo 4 and show their addition and multiplication. What is the result of each operation?
Keep track of modulo operations throughout.
Prove that the product of a polynomial of degree m and another of degree n has a degree of m+n.
Visualize the polynomial terms’ expansion.
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