(10x^(3)-5x^(2)-6x)/(2x^(2))

Simplify Expression: Simplify the expression by dividing each term in the numerator by the term in the denominator. We have the expression (10x^(3)-5x^(2)-6x)/(2x^(2)). We will divide each term in the numerator by 2x^(2).Divide 10x^3 by 2x^2: Divide the first term 10x^(3) by 2x^(2). 10x^(3) / 2x^(2) = (10/2) * (x^(3)/x^(2)) = 5x^(3-2) = 5x.Divide -5x^2 by 2x^2: Divide the second term -5x^(2) by 2x^(2). -5x^(2) / 2x^(2) = (-5/2) * (x^(2)/x^(2)) = -5/2.Divide -6x by 2x^2: Divide the third term -6x by 2x^(2). -6x / 2x^(2) = (-6/2) * (x/x^(2)) = -3/x.Combine Results: Combine the results from steps 2, 3, and 4 to get the final simplified expression. The simplified expression is 5x - 5/2 - 3/x.

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$\left(10x^{3}-5x^{2}-6x\right)\div\left(2x^{2}\right)$

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\left(10x^{3}-5x^{2}-6x\right)\div\left(2x^{2}\right)

Simplify Expression: Simplify the expression by dividing each term in the numerator by the term in the denominator. $\newline$ We have the expression $(10x^{3}-5x^{2}-6x)/(2x^{2})$ . We will divide each term in the numerator by $2x^{2}$ .
Divide $10x^3$ by $2x^2$ : Divide the first term $10x^{3}$ by $2x^{2}$ . $10x^{3} / 2x^{2} = (10/2) \cdot (x^{3}/x^{2}) = 5x^{3-2} = 5x$ .
Divide $-5x^2$ by $2x^2$ : Divide the second term $-5x^{2}$ by $2x^{2}$ . $\newline$ $-5x^{2} / 2x^{2} = (-5/2) \times (x^{2}/x^{2}) = -5/2$ .
Divide $-6x$ by $2x^2$ : Divide the third term $-6x$ by $2x^{2}$ . $\newline$ $-6x / 2x^{2} = (-6/2) \cdot (x/x^{2}) = -3/x$ .
Combine Results: Combine the results from steps $2$ , $3$ , and $4$ to get the final simplified expression. $\newline$ The simplified expression is $5x - \frac{5}{2} - \frac{3}{x}.$