Polynomials

Question

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(a) Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^5 - 6x^2 + 4x - 1. Let a be a constant. What is the largest possible degree of f(x) + a*g(x)?

(b) Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^5 - 6x^2 + 4x - 1. Let b be a constant. What is the smallest possible degree of f(x) + b*g(x)?

Guest Sep 20, 2021

Melody · Answer 1 · 2021-09-20T02:41:36

The degree of f(x)+kg(x) will be 5 unless k=0.

If k=0 then f(x)+kg(x)=f(x) and so the degree will be 4