Algebra Examples

$(10 c^{6} + 6 c^{5} - 24 c) \div (- c^{4})$

Step 1

Rewrite the division as a fraction.

$\frac{10 c^{6} + 6 c^{5} - 24 c}{- c^{4}}$

Step 2

Factor $2 c$ out of $10 c^{6} + 6 c^{5} - 24 c$ .

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Step 2.1

Factor $2 c$ out of $10 c^{6}$ .

$\frac{2 c (5 c^{5}) + 6 c^{5} - 24 c}{- c^{4}}$

Step 2.2

Factor $2 c$ out of $6 c^{5}$ .

$\frac{2 c (5 c^{5}) + 2 c (3 c^{4}) - 24 c}{- c^{4}}$

Step 2.3

Factor $2 c$ out of $- 24 c$ .

$\frac{2 c (5 c^{5}) + 2 c (3 c^{4}) + 2 c (- 12)}{- c^{4}}$

Step 2.4

Factor $2 c$ out of $2 c (5 c^{5}) + 2 c (3 c^{4})$ .

$\frac{2 c (5 c^{5} + 3 c^{4}) + 2 c (- 12)}{- c^{4}}$

Step 2.5

Factor $2 c$ out of $2 c (5 c^{5} + 3 c^{4}) + 2 c (- 12)$ .

$\frac{2 c (5 c^{5} + 3 c^{4} - 12)}{- c^{4}}$

Step 3

Cancel the common factor of $c$ and $c^{4}$ .

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Step 3.1

Factor $c$ out of $2 c (5 c^{5} + 3 c^{4} - 12)$ .

$\frac{c (2 (5 c^{5} + 3 c^{4} - 12))}{- c^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $c$ out of $- c^{4}$ .

$\frac{c (2 (5 c^{5} + 3 c^{4} - 12))}{c (- c^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{c (2 (5 c^{5} + 3 c^{4} - 12))}{c (- c^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 (5 c^{5} + 3 c^{4} - 12)}{- c^{3}}$

Step 4

Move the negative in front of the fraction.

$- \frac{2 (5 c^{5} + 3 c^{4} - 12)}{c^{3}}$

Step 5

Apply the distributive property.

$- \frac{2 (5 c^{5}) + 2 (3 c^{4}) + 2 \cdot - 12}{c^{3}}$

Step 6

Simplify.

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Step 6.1

Multiply $5$ by $2$ .

$- \frac{10 c^{5} + 2 (3 c^{4}) + 2 \cdot - 12}{c^{3}}$

Step 6.2

Multiply $3$ by $2$ .

$- \frac{10 c^{5} + 6 c^{4} + 2 \cdot - 12}{c^{3}}$

Step 6.3

Multiply $2$ by $- 12$ .

$- \frac{10 c^{5} + 6 c^{4} - 24}{c^{3}}$

Step 7

Split the fraction $\frac{10 c^{5} + 6 c^{4} - 24}{c^{3}}$ into two fractions.

$- (\frac{10 c^{5} + 6 c^{4}}{c^{3}} + \frac{- 24}{c^{3}})$

Step 8

Split the fraction $\frac{10 c^{5} + 6 c^{4}}{c^{3}}$ into two fractions.

$- (\frac{10 c^{5}}{c^{3}} + \frac{6 c^{4}}{c^{3}} + \frac{- 24}{c^{3}})$

Step 9

Cancel the common factor of $c^{5}$ and $c^{3}$ .

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Step 9.1

Factor $c^{3}$ out of $10 c^{5}$ .

$- (\frac{c^{3} (10 c^{2})}{c^{3}} + \frac{6 c^{4}}{c^{3}} + \frac{- 24}{c^{3}})$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Multiply by $1$ .

$- (\frac{c^{3} (10 c^{2})}{c^{3} \cdot 1} + \frac{6 c^{4}}{c^{3}} + \frac{- 24}{c^{3}})$

Step 9.2.2

Cancel the common factor.

$- (\frac{c^{3} (10 c^{2})}{c^{3} \cdot 1} + \frac{6 c^{4}}{c^{3}} + \frac{- 24}{c^{3}})$

Step 9.2.3

Rewrite the expression.

$- (\frac{10 c^{2}}{1} + \frac{6 c^{4}}{c^{3}} + \frac{- 24}{c^{3}})$

Step 9.2.4

Divide $10 c^{2}$ by $1$ .

$- (10 c^{2} + \frac{6 c^{4}}{c^{3}} + \frac{- 24}{c^{3}})$

Step 10

Cancel the common factor of $c^{4}$ and $c^{3}$ .

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Step 10.1

Factor $c^{3}$ out of $6 c^{4}$ .

$- (10 c^{2} + \frac{c^{3} (6 c)}{c^{3}} + \frac{- 24}{c^{3}})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Multiply by $1$ .

$- (10 c^{2} + \frac{c^{3} (6 c)}{c^{3} \cdot 1} + \frac{- 24}{c^{3}})$

Step 10.2.2

Cancel the common factor.

$- (10 c^{2} + \frac{c^{3} (6 c)}{c^{3} \cdot 1} + \frac{- 24}{c^{3}})$

Step 10.2.3

Rewrite the expression.

$- (10 c^{2} + \frac{6 c}{1} + \frac{- 24}{c^{3}})$

Step 10.2.4

Divide $6 c$ by $1$ .

$- (10 c^{2} + 6 c + \frac{- 24}{c^{3}})$

Step 11

Move the negative in front of the fraction.

$- (10 c^{2} + 6 c - \frac{24}{c^{3}})$