jmc

Question

Suppose f(z) and g(z) are polynomials in z, and the degree of g(z) is less than the degree of f(z). If the degree of f(z) is two, what is the degree of f(z)+g(z)?

Accepted Answer

We have f(z)=a_2 z^2+a_1 z+a_0, and g(z)=b_1 z+b_0, where a_2 is nonzero. Then f(z)+g(z)=a_2 z^2+(a_1+b_1) z+(a_0+b_0). The degree of this polynomial is 2.