If $f(x)$ is a polynomial of degree 7, and $g(x)$ is a polynomial of degree 7, then what is the product of the minimum and the maximum possible degrees of $f(x) + g(x)$?

Guest Mar 20, 2020

#1**+1 **

If you add two polynomials together, you cannot end with a polynomial of higher degree than the highest degree one you started with.

Therefore, the maximum possible degree of the sum of two seven-degree polynomials is seven.

However, you can end with a polynomial that has a lower degree; so, if you start with two seven-degree polynomials, you can end with a sum that has any degree from seven down to zero.

For example: if f(x) = 3x^{7} + 16x^{2} - 9 while g(x) = -3x^{7 }- 16x^{2} + 2, the sum of the two polynomials is -7, a constant polynomial that has degree zero.

So, the product would be zero.

geno3141 Mar 20, 2020