jmc

Question

If f(x) is a polynomial of degree 4, and g(x) is a polynomial of degree 2, then what is the degree of polynomial f(x) - g(x)?

Accepted Answer

Let f(x) = a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0 and g(x) = b_2 x^2 + b_1 x + b_0. Then align* & f(x) - g(x) &= (a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0) - (b_2 x^2 + b_1 x + b_0) &= a_4 x^4 + a_3 x^3 + (a_2 - b_2) x^2 + (a_1 - b_1) x + (a_0 - b_0). align*Thus, the degree of f(x) - g(x) is 4.