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d: \(\left(6x-5x^2-15+2x^3\right):\left(2x-5\right)\)
\(=\frac{2x^3-5x^2+6x-15}{2x-5}\)
\(=\frac{x^2\left(2x-5\right)+3\left(2x-5\right)}{2x-5}=x^2+3\)
e: \(\left(x^3+x^5+x^2+1\right):\left(x^3+1\right)\)
\(=\frac{x^5+x^3+x^2+1}{x^3+1}=\frac{x^2\left(x^3+1\right)+\left(x^3+1\right)}{x^3+1}\)
\(=x^2+1\)
i: \(\left(3-2x+2x^3+5x^2\right):\left(2x^2-x+1\right)\)
\(=\frac{2x^3+5x^2-2x+3}{2x^2-x+1}=\frac{2x^3-x^2+x+6x^2-3x+3}{2x^2-x+1}\)
\(=\frac{x\left(2x^2-x+1\right)+3\left(2x^2-x+1\right)}{2x^2-x+1}=x+3\)
a, \(5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)=5.\left(x-y\right)^2\)
b, \(x^2-4x+4-y^2=\left(x^2-4x+4\right)-y^2=\left(x-2\right)^2-y^2\)
\(=\left(x-2-y\right)\left(x-2+y\right)\)
c, \(3x^2-2x-5=3x^2-5x+3x-5=x\left(3x-5\right)+3x-5\)
\(=\left(3x-5\right)\left(x+1\right)\)
\(3x^5-x^2+2x^3-6x^4+2=3x^5-6x^4+2x^3-x^2+2 \)
Có : \(\frac{3x^5-6x^4+2x^3-x^2+2}{3x^2+2}=\frac{x^3.\left(3x^2+2\right)-6x^4-x^2+2}{3x^2+2}=\frac{...-3x^2.2x^2-4x^2+3x^2+2}{3x^2+2}\)
\(=\frac{...-2x^2.\left(3x^2+2\right)+\left(3x^2+2\right)}{3x^2+2}=\frac{\left(x^3-2x^2+1\right).\left(3x^2+2\right)}{3x^2+2}=x^3-2x^2+1\)
\(\dfrac{x^5-3x^4+5x^3-x^2+3x-5}{x^2-3x+5}\)
\(=\dfrac{x^3\left(x^2-3x+5\right)-\left(x^2-3x+5\right)}{x^2-3x+5}\)
\(=x^3-1\)