Question

If f(x) = 3х^2 and g(x) = 4х^3 + 1, what is the degree of (f•g)(x)?

Answer 1

$\bf \begin{cases} f(x)=3x^2\\ g(x)=4x^3+1 \end{cases}\qquad (f\cdot g)(x)\implies f(x)\cdot g(x)\implies [3x^2]\cdot [4x^3+1] \\\\\\ 12x^2x^3+3x^2\implies 12x^{2+3}3x^2\implies \stackrel{\textit{5th degree}}{12x^{\stackrel{\downarrow }{5}}+3x^2}$