Pre-Algebra Examples

$(- 20 k^{2} - 15 k + 25) \div 5 k$

Step 1

Rewrite the division as a fraction.

$\frac{- 20 k^{2} - 15 k + 25}{5 k}$

Step 2

Cancel the common factor of $- 20 k^{2} - 15 k + 25$ and $5$ .

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Step 2.1

Factor $5$ out of $- 20 k^{2}$ .

$\frac{5 (- 4 k^{2}) - 15 k + 25}{5 k}$

Step 2.2

Factor $5$ out of $- 15 k$ .

$\frac{5 (- 4 k^{2}) + 5 (- 3 k) + 25}{5 k}$

Step 2.3

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

$\frac{5 (- 4 k^{2} - 3 k) + 25}{5 k}$

Step 2.4

Factor $5$ out of $25$ .

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

Step 2.5

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

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

Step 2.6

Cancel the common factors.

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Step 2.6.1

Factor $5$ out of $5 k$ .

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

Step 2.6.2

Cancel the common factor.

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

Step 2.6.3

Rewrite the expression.

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

Step 3

Factor $- 1$ out of $- 4 k^{2}$ .

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

Step 4

Factor $- 1$ out of $- 3 k$ .

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

Step 5

Factor $- 1$ out of $- (4 k^{2}) - (3 k)$ .

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

Step 6

Rewrite $5$ as $- 1 (- 5)$ .

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

Step 7

Factor $- 1$ out of $- (4 k^{2} + 3 k) - 1 (- 5)$ .

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

Step 8

Rewrite $- (4 k^{2} + 3 k - 5)$ as $- 1 (4 k^{2} + 3 k - 5)$ .

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

Step 9

Move the negative in front of the fraction.

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

Step 10

Split the fraction $\frac{4 k^{2} + 3 k - 5}{k}$ into two fractions.

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

Step 11

Split the fraction $\frac{4 k^{2} + 3 k}{k}$ into two fractions.

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

Step 12

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

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Step 12.1

Factor $k$ out of $4 k^{2}$ .

$- (\frac{k (4 k)}{k} + \frac{3 k}{k} + \frac{- 5}{k})$

Step 12.2

Cancel the common factors.

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Step 12.2.1

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

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

Step 12.2.2

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

$- (\frac{k (4 k)}{k \cdot 1} + \frac{3 k}{k} + \frac{- 5}{k})$

Step 12.2.3

Cancel the common factor.

$- (\frac{k (4 k)}{k \cdot 1} + \frac{3 k}{k} + \frac{- 5}{k})$

Step 12.2.4

Rewrite the expression.

$- (\frac{4 k}{1} + \frac{3 k}{k} + \frac{- 5}{k})$

Step 12.2.5

Divide $4 k$ by $1$ .

$- (4 k + \frac{3 k}{k} + \frac{- 5}{k})$

Step 13

Cancel the common factor of $k$ .

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Step 13.1

Cancel the common factor.

$- (4 k + \frac{3 k}{k} + \frac{- 5}{k})$

Step 13.2

Divide $3$ by $1$ .

$- (4 k + 3 + \frac{- 5}{k})$

Step 14

Move the negative in front of the fraction.

$- (4 k + 3 - \frac{5}{k})$