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 $f(x) + g(x)$?
+23246 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) = 3x7 + 16x2 - 9 while g(x) = -3x7 - 16x2 + 2, the sum of the two polynomials is -7, a constant polynomial that has degree zero.
So, the product would be zero.
