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

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

also if you could explane what degree means in functions that would be great too :)

Any help will be great.

THX IN ADVANCE \(:)\)

srry for all the changes.

Guest Aug 21, 2019

edited by
Guest
Aug 21, 2019

edited by Guest Aug 21, 2019

edited by Guest Aug 21, 2019

edited by Guest Aug 21, 2019

edited by Guest Aug 21, 2019

#1**0 **

\(1) ~1 + 5 = 6\\~\\ 2)~\text{The degree of a polynomial $f(x)$ is its highest power of $x$ $\\f(x)+bg(x)$ will be of degree 4}\)

.Rom Aug 21, 2019