Question 4: Find the natural number n so that polynomial A is divisible by polynomial B \(A=4 x^{n+1} y^{2} ; B=3 x^{3} y^{n- first}\)

We have

\(\frac{A}{B}=\frac{4 x^{n+1} y^{2}}{3 x^{3} y^{n-1}}\)

Polynomial A is divisible by polynomial\(\mathrm{B} \Leftrightarrow\left\{\begin{array}{l}n+1 \geq 3 \\ 2 \geq n-1\end{array} \Leftrightarrow\left\{\begin{array }{l}n \geq 2 \\ n \leq 3\end{array} \Leftrightarrow\left[\begin{array}{l}n=2\\n=3\end{array}\right\right\right\)[\begin{array}{l}n=2\n=3\end{array}\right\right\right\)