Algebra Examples

$(8 x^{3} + 5 x^{2} + 3 x - 1) \div 2 x$

Step 1

Rewrite the division as a fraction.

$\frac{8 x^{3} + 5 x^{2} + 3 x - 1}{2 x}$

Step 2

Split the fraction $\frac{8 x^{3} + 5 x^{2} + 3 x - 1}{2 x}$ into two fractions.

$\frac{8 x^{3} + 5 x^{2} + 3 x}{2 x} + \frac{- 1}{2 x}$

Step 3

Split the fraction $\frac{8 x^{3} + 5 x^{2} + 3 x}{2 x}$ into two fractions.

$\frac{8 x^{3} + 5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 4

Split the fraction $\frac{8 x^{3} + 5 x^{2}}{2 x}$ into two fractions.

$\frac{8 x^{3}}{2 x} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 5

Cancel the common factor of $8$ and $2$ .

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Step 5.1

Factor $2$ out of $8 x^{3}$ .

$\frac{2 (4 x^{3})}{2 x} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2 x$ .

$\frac{2 (4 x^{3})}{2 (x)} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (4 x^{3})}{2 x} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 5.2.3

Rewrite the expression.

$\frac{4 x^{3}}{x} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 6

Cancel the common factor of $x^{3}$ and $x$ .

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Step 6.1

Factor $x$ out of $4 x^{3}$ .

$\frac{x (4 x^{2})}{x} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Raise $x$ to the power of $1$ .

$\frac{x (4 x^{2})}{x^{1}} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 6.2.2

Factor $x$ out of $x^{1}$ .

$\frac{x (4 x^{2})}{x \cdot 1} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 6.2.3

Cancel the common factor.

$\frac{x (4 x^{2})}{x \cdot 1} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 6.2.4

Rewrite the expression.

$\frac{4 x^{2}}{1} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 6.2.5

Divide $4 x^{2}$ by $1$ .

$4 x^{2} + \frac{5 x^{2}}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 7

Cancel the common factor of $x^{2}$ and $x$ .

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Step 7.1

Factor $x$ out of $5 x^{2}$ .

$4 x^{2} + \frac{x (5 x)}{2 x} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $x$ out of $2 x$ .

$4 x^{2} + \frac{x (5 x)}{x \cdot 2} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 7.2.2

Cancel the common factor.

$4 x^{2} + \frac{x (5 x)}{x \cdot 2} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 7.2.3

Rewrite the expression.

$4 x^{2} + \frac{5 x}{2} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 8

Cancel the common factor of $x$ .

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Step 8.1

Cancel the common factor.

$4 x^{2} + \frac{5 x}{2} + \frac{3 x}{2 x} + \frac{- 1}{2 x}$

Step 8.2

Rewrite the expression.

$4 x^{2} + \frac{5 x}{2} + \frac{3}{2} + \frac{- 1}{2 x}$

Step 9

Move the negative in front of the fraction.

$4 x^{2} + \frac{5 x}{2} + \frac{3}{2} - \frac{1}{2 x}$