[tex]\frac{10x^4+25x^3+8x^2+6x-17}{2x^2+3x-5}[/tex]
[tex]=5x^2+\frac{10x^3+33x^2+6x-17}{2x^2+3x-5}[/tex]
[tex]=5x^2+5x+\frac{18x^2+31x-17}{2x^2+3x-5}[/tex]
[tex]\boxed{ =5x^2+5x+9+\frac{4x+28}{2x^2+3x-5}}[/tex]
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DIVIDIR
[tex]\frac{10x^4+25x^3+8x^2+6x-17}{2x^2+3x-5}[/tex]
DIVIDIR
[tex]=5x^2+\frac{10x^3+33x^2+6x-17}{2x^2+3x-5}[/tex]
DIVIDIR
[tex]=5x^2+5x+\frac{18x^2+31x-17}{2x^2+3x-5}[/tex]
RESULTADO
[tex]\boxed{ =5x^2+5x+9+\frac{4x+28}{2x^2+3x-5}}[/tex]