Basic Math Examples

$(10 w^{4} + 15 w - 5 w^{2}) \div 5 w$

Step 1

Rewrite the division as a fraction.

$\frac{10 w^{4} + 15 w - 5 w^{2}}{5 w}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $5 w$ out of $10 w^{4} + 15 w - 5 w^{2}$ .

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Step 2.1.1

Factor $5 w$ out of $10 w^{4}$ .

$\frac{5 w (2 w^{3}) + 15 w - 5 w^{2}}{5 w}$

Step 2.1.2

Factor $5 w$ out of $15 w$ .

$\frac{5 w (2 w^{3}) + 5 w (3) - 5 w^{2}}{5 w}$

Step 2.1.3

Factor $5 w$ out of $- 5 w^{2}$ .

$\frac{5 w (2 w^{3}) + 5 w (3) + 5 w (- w)}{5 w}$

Step 2.1.4

Factor $5 w$ out of $5 w (2 w^{3}) + 5 w (3)$ .

$\frac{5 w (2 w^{3} + 3) + 5 w (- w)}{5 w}$

Step 2.1.5

Factor $5 w$ out of $5 w (2 w^{3} + 3) + 5 w (- w)$ .

$\frac{5 w (2 w^{3} + 3 - w)}{5 w}$

Step 2.2

Reorder terms.

$\frac{5 w (2 w^{3} - w + 3)}{5 w}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $5$ .

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Step 3.1.1

Cancel the common factor.

$\frac{5 w (2 w^{3} - w + 3)}{5 w}$

Step 3.1.2

Rewrite the expression.

$\frac{w (2 w^{3} - w + 3)}{w}$

Step 3.2

Cancel the common factor of $w$ .

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Step 3.2.1

Cancel the common factor.

$\frac{w (2 w^{3} - w + 3)}{w}$

Step 3.2.2

Divide $2 w^{3} - w + 3$ by $1$ .

$2 w^{3} - w + 3$