Let $f(x) = x^3 + 3x^2 + 4x - 7$ and $g(x) = 2x^8 - 8x^7 + 4x^6 - x^5$. What is the coefficient of $x^2$ in the sum $f(x) + g(x)$?

RedDragonl May 25, 2024

#1**-1 **

When we add f(x) and g(x), we get \(2 x^ 8 − 8 x^ 7 + 4 x^ 6 − x^ 5 + x^ 3 + 3 x^ 2 + 4 x − 7\). The coefficient would be 3.

However, notice that the coefficient stays the same in f(x). This is because g(x) doesn't have a term with x^2, so our asnwer is the same coefficient as in f(x).

Thanks! :)

NotThatSmart May 25, 2024