Mk làm chi tiết từng bc một nên hơi dài
~ học tốt ~
\(\frac{x^3-4x^2+x+6}{x-2}\)
\(=\frac{x^3-2x^2-2x^2+x+6}{x-2}\)
\(=\frac{\left(x^3-2x^2\right)-\left(2x^2-x-6\right)}{x-2}\)
\(=\frac{x^2\left(x-2\right)-\left(2x^2-4x+3x-6\right)}{x-2}\)
\(=\frac{x^2\left(x-2\right)-[\left(2x^2-4x\right)+\left(3x-6\right)]}{x-2}\)
\(=\frac{x^2\left(x-2\right)-[2x\left(x-2\right)+3\left(x-2\right)]}{x-2}\)
\(=\frac{x^2\left(x-2\right)-\left(x-2\right)\left(2x+3\right)}{x-2}\)
\(=\frac{\left(x-2\right)\left(x^2-2x-3\right)}{x-2}\)
\(=\frac{\left(x-2\right)\left(x^2+x-3x-3\right)}{x-2}\)
\(=\frac{\left(x-2\right)[\left(x^2+x\right)-\left(3x-3\right)]}{x-2}\)
\(=\frac{\left(x-2\right)[x\left(x-1\right)-3\left(x-1\right)}{x-2}\)
\(=\frac{\left(x-2\right)\left(x-1\right)\left(x-3\right)}{x-2}\)
\(=\left(x-1\right)\left(x-3\right)\)
\(\frac{x^3-4x^2+x+6}{x-2}\)
\(=\frac{x^3-2x^2-2x^2+x+6}{x-2}\)
\(=\frac{x^2\left(x-2\right)-\left(x-2\right)\left(2x+3\right)}{x-2}\)
\(=\frac{\left(x-2\right)\left(x^2-2x-3\right)}{x-2}\)
\(=x^2-2x-3\)
@TrầnMinhPhong.
Đến đoạn này là được rồi .
