Đáp án:
$a)\left[\begin{array}{l} n=2\\ n = 3\end{array} \right. \\ b)\left[\begin{array}{l} n=3\\ n = 4\end{array} \right. \\ c) n=2$
Giải thích các bước giải:
$a)A=4x^{n+1}y^2; B=3x^3y^{n-1}\\ A:B=4x^{n+1}y^2:(3x^3y^{n-1})=\dfrac{4}{3}x^{n+1-3}y{2-(n-1)}=\dfrac{4}{3}x^{n-2}y^{3-n}\\ A \ \vdots \ B \Rightarrow \left\{\begin{array}{l} n-2 \ge 0\\ 3-n \ge 0\\ n \in \mathbb{N}\end{array} \right. \Leftrightarrow\left\{\begin{array}{l} n \ge 2\\ n \le 3\\ n \in \mathbb{N}\end{array} \right. \Leftrightarrow\left[\begin{array}{l} n=2\\ n = 3\end{array} \right. \\ b)A=7x^{n-1}y^5-5x^3y^4; B=5x^2y^n\\ A:B=(7x^{n-1}y^5-5x^3y^4):(5x^2y^n)=\dfrac{7}{5}x^{n-3}y^{5-n}-xy^{4-n}\\ A \ \vdots \ B \Rightarrow \left\{\begin{array}{l} n-3 \ge 0\\ 5-n \ge 0 \\ 4 -n \ge 0\\ n \in \mathbb{N}\end{array} \right. \left\{\begin{array}{l} n \ge 3\\ n \le 5 \\ n \le 4 \\ n \in \mathbb{N}\end{array} \right. \Leftrightarrow\left[\begin{array}{l} n=3\\ n = 4\end{array} \right. \\ c)A=x^4y^3+3x^3y^3+x^2y^n; B=4x^ny^2\\ A:B=(x^4y^3+3x^3y^3+x^2y^n):(4x^ny^2)=\dfrac{1}{4}(x^{4-n}y+3x^{3-n}y+x^{2-n}y^{n-2}\\ A \ \vdots \ B \Rightarrow \left\{\begin{array}{l} 4-n \ge 0\\ 3-n \ge 0 \\2-n\ge 0\\ n-2 \ge 0 \\ n \in \mathbb{N}\end{array} \right. \Leftrightarrow \left\{\begin{array}{l} n \le 4\\n \le 3 \\n \le 2\\ n\ge 2 \\ n \in \mathbb{N}\end{array} \right. \Leftrightarrow n=2$
