Basic Math Examples

$(- 5 r^{6} - 6 r^{5} - 5 r^{4} + 3 r^{3} - 5 r^{2} + 6 r + 5) \div (r - 1)$

Step 1

Rewrite the division as a fraction.

$\frac{- 5 r^{6} - 6 r^{5} - 5 r^{4} + 3 r^{3} - 5 r^{2} + 6 r + 5}{r - 1}$

Step 2

Factor $- 1$ out of $- 5 r^{6}$ .

$\frac{- (5 r^{6}) - 6 r^{5} - 5 r^{4} + 3 r^{3} - 5 r^{2} + 6 r + 5}{r - 1}$

Step 3

Factor $- 1$ out of $- 6 r^{5}$ .

$\frac{- (5 r^{6}) - (6 r^{5}) - 5 r^{4} + 3 r^{3} - 5 r^{2} + 6 r + 5}{r - 1}$

Step 4

Factor $- 1$ out of $- (5 r^{6}) - (6 r^{5})$ .

$\frac{- (5 r^{6} + 6 r^{5}) - 5 r^{4} + 3 r^{3} - 5 r^{2} + 6 r + 5}{r - 1}$

Step 5

Factor $- 1$ out of $- 5 r^{4}$ .

$\frac{- (5 r^{6} + 6 r^{5}) - (5 r^{4}) + 3 r^{3} - 5 r^{2} + 6 r + 5}{r - 1}$

Step 6

Factor $- 1$ out of $- (5 r^{6} + 6 r^{5}) - (5 r^{4})$ .

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4}) + 3 r^{3} - 5 r^{2} + 6 r + 5}{r - 1}$

Step 7

Factor $- 1$ out of $3 r^{3}$ .

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4}) - (- 3 r^{3}) - 5 r^{2} + 6 r + 5}{r - 1}$

Step 8

Factor $- 1$ out of $- (5 r^{6} + 6 r^{5} + 5 r^{4}) - (- 3 r^{3})$ .

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3}) - 5 r^{2} + 6 r + 5}{r - 1}$

Step 9

Factor $- 1$ out of $- 5 r^{2}$ .

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3}) - (5 r^{2}) + 6 r + 5}{r - 1}$

Step 10

Factor $- 1$ out of $- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3}) - (5 r^{2})$ .

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2}) + 6 r + 5}{r - 1}$

Step 11

Factor $- 1$ out of $6 r$ .

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2}) - (- 6 r) + 5}{r - 1}$

Step 12

Factor $- 1$ out of $- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2}) - (- 6 r)$ .

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2} - 6 r) + 5}{r - 1}$

Step 13

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

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2} - 6 r) - 1 (- 5)}{r - 1}$

Step 14

Factor $- 1$ out of $- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2} - 6 r) - 1 (- 5)$ .

$\frac{- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2} - 6 r - 5)}{r - 1}$

Step 15

Simplify the expression.

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Step 15.1

Rewrite $- (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2} - 6 r - 5)$ as $- 1 (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2} - 6 r - 5)$ .

$\frac{- 1 (5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2} - 6 r - 5)}{r - 1}$

Step 15.2

Move the negative in front of the fraction.

$- \frac{5 r^{6} + 6 r^{5} + 5 r^{4} - 3 r^{3} + 5 r^{2} - 6 r - 5}{r - 1}$