Guided Practice: Polynomial Functions and Rates of Change

A nonconstant polynomial function of x is any function representation equivalent to a_nxⁿ + a_n−1xⁿ⁻¹ + … + a₂x² + a₁x + a₀, where n is a positive integer, each a_i is a real number, and a_n is nonzero. The degree is n, the leading term is a_nxⁿ, and the leading coefficient is a_n.

Let p(x) = 6x² − 4x⁷ + x − 3. Is p a polynomial function? Name its degree, leading term, and leading coefficient.

Try it on paper first, then reveal each step to check your work.