Algebra Examples

$(6 p^{3} + 150 p^{2} + 5 p) \div 15 p$

Step 1

Rewrite the division as a fraction.

$\frac{6 p^{3} + 150 p^{2} + 5 p}{15 p}$

Step 2

Factor $p$ out of $6 p^{3} + 150 p^{2} + 5 p$ .

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Step 2.1

Factor $p$ out of $6 p^{3}$ .

$\frac{p (6 p^{2}) + 150 p^{2} + 5 p}{15 p}$

Step 2.2

Factor $p$ out of $150 p^{2}$ .

$\frac{p (6 p^{2}) + p (150 p) + 5 p}{15 p}$

Step 2.3

Factor $p$ out of $5 p$ .

$\frac{p (6 p^{2}) + p (150 p) + p \cdot 5}{15 p}$

Step 2.4

Factor $p$ out of $p (6 p^{2}) + p (150 p)$ .

$\frac{p (6 p^{2} + 150 p) + p \cdot 5}{15 p}$

Step 2.5

Factor $p$ out of $p (6 p^{2} + 150 p) + p \cdot 5$ .

$\frac{p (6 p^{2} + 150 p + 5)}{15 p}$

Step 3

Cancel the common factor of $p$ .

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Step 3.1

Cancel the common factor.

$\frac{p (6 p^{2} + 150 p + 5)}{15 p}$

Step 3.2

Rewrite the expression.

$\frac{6 p^{2} + 150 p + 5}{15}$

Step 4

Split the fraction $\frac{6 p^{2} + 150 p + 5}{15}$ into two fractions.

$\frac{6 p^{2} + 150 p}{15} + \frac{5}{15}$

Step 5

Split the fraction $\frac{6 p^{2} + 150 p}{15}$ into two fractions.

$\frac{6 p^{2}}{15} + \frac{150 p}{15} + \frac{5}{15}$

Step 6

Cancel the common factor of $6$ and $15$ .

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Step 6.1

Factor $3$ out of $6 p^{2}$ .

$\frac{3 (2 p^{2})}{15} + \frac{150 p}{15} + \frac{5}{15}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $15$ .

$\frac{3 (2 p^{2})}{3 (5)} + \frac{150 p}{15} + \frac{5}{15}$

Step 6.2.2

Cancel the common factor.

$\frac{3 (2 p^{2})}{3 \cdot 5} + \frac{150 p}{15} + \frac{5}{15}$

Step 6.2.3

Rewrite the expression.

$\frac{2 p^{2}}{5} + \frac{150 p}{15} + \frac{5}{15}$

Step 7

Cancel the common factor of $150$ and $15$ .

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Step 7.1

Factor $15$ out of $150 p$ .

$\frac{2 p^{2}}{5} + \frac{15 (10 p)}{15} + \frac{5}{15}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $15$ out of $15$ .

$\frac{2 p^{2}}{5} + \frac{15 (10 p)}{15 (1)} + \frac{5}{15}$

Step 7.2.2

Cancel the common factor.

$\frac{2 p^{2}}{5} + \frac{15 (10 p)}{15 \cdot 1} + \frac{5}{15}$

Step 7.2.3

Rewrite the expression.

$\frac{2 p^{2}}{5} + \frac{10 p}{1} + \frac{5}{15}$

Step 7.2.4

Divide $10 p$ by $1$ .

$\frac{2 p^{2}}{5} + 10 p + \frac{5}{15}$

Step 8

Cancel the common factor of $5$ and $15$ .

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Step 8.1

Factor $5$ out of $5$ .

$\frac{2 p^{2}}{5} + 10 p + \frac{5 (1)}{15}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $5$ out of $15$ .

$\frac{2 p^{2}}{5} + 10 p + \frac{5 \cdot 1}{5 \cdot 3}$

Step 8.2.2

Cancel the common factor.

$\frac{2 p^{2}}{5} + 10 p + \frac{5 \cdot 1}{5 \cdot 3}$

Step 8.2.3

Rewrite the expression.

$\frac{2 p^{2}}{5} + 10 p + \frac{1}{3}$