Bài 1:
a) Ta có: \(\left(x^2-2x+1\right):\left(x-1\right)\)
\(=\left(x-1\right)^2:\left(x-1\right)\)
=x-1
b) Ta có: \(\left(x^3+1\right):\left(x^2-x+1\right)\)
\(=\frac{\left(x+1\right)\left(x^2-x+1\right)}{x^2-x+1}=x+1\)
c) Ta có: \(\left(x^3-x^2-5x-3\right):\left(x-3\right)\)
\(=\frac{x^3-3x^2+2x^2-6x+x-3}{x-3}\)
\(=\frac{x^2\left(x-3\right)+2x\left(x-3\right)+\left(x-3\right)}{\left(x-3\right)}\)
\(=\frac{\left(x-3\right)\left(x^2+2x+1\right)}{\left(x-3\right)}\)
\(=\left(x+1\right)^2\)
d) Ta có: \(\left(x^4+x^3-6x^2-5x+5\right):\left(x^2+x-1\right)\)
\(=\frac{x^4+x^3-x^2-5x^2-5x+5}{x^2+x-1}\)
\(=\frac{x^2\left(x^2+x-1\right)-5\left(x^2+x-1\right)}{x^2+x-1}\)
\(=\frac{\left(x^2+x-1\right)\left(x^2-5\right)}{x^2+x-1}\)
\(=x^2-5\)
