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.
+6248 \(1) ~1 + 5 = 6\\~\\ 2)~\text{The degree of a polynomial $f(x)$ is its highest power of $x$ $\\f(x)+bg(x)$ will be of degree 4}\)
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