Solve 5frac{27x^{10}-21x^9-12x^7-3x^4}{-3x^3}

$$5 \frac { 27 x ^ { 10 } - 21 x ^ { 9 } - 12 x ^ { 7 } - 3 x ^ { 4 } } { - 3 x ^ { 3 } }$$

Evaluate

$$5x+20x^{4}+35x^{6}-45x^{7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{27x^{10}-21x^{9}-12x^{7}-3x^{4}}{-3x^{3}}.

$$5\times \frac{3x^{4}\left(9x^{6}-7x^{5}-4x^{3}-1\right)}{-3x^{3}}$$

Cancel out 3x^{3} in both numerator and denominator.

$$5\times \frac{x\left(9x^{6}-7x^{5}-4x^{3}-1\right)}{-1}$$

Anything divided by -1 gives its opposite.

$$5\left(-x\left(9x^{6}-7x^{5}-4x^{3}-1\right)\right)$$

Use the distributive property to multiply x by 9x^{6}-7x^{5}-4x^{3}-1.

$$5\left(-\left(9x^{7}-7x^{6}-4x^{4}-x\right)\right)$$

To find the opposite of 9x^{7}-7x^{6}-4x^{4}-x, find the opposite of each term.

$$5\left(-9x^{7}+7x^{6}+4x^{4}+x\right)$$

Use the distributive property to multiply 5 by -9x^{7}+7x^{6}+4x^{4}+x.

$$-45x^{7}+35x^{6}+20x^{4}+5x$$

Expand

$$5x+20x^{4}+35x^{6}-45x^{7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{27x^{10}-21x^{9}-12x^{7}-3x^{4}}{-3x^{3}}.

$$5\times \frac{3x^{4}\left(9x^{6}-7x^{5}-4x^{3}-1\right)}{-3x^{3}}$$

Cancel out 3x^{3} in both numerator and denominator.

$$5\times \frac{x\left(9x^{6}-7x^{5}-4x^{3}-1\right)}{-1}$$

Anything divided by -1 gives its opposite.

$$5\left(-x\left(9x^{6}-7x^{5}-4x^{3}-1\right)\right)$$

Use the distributive property to multiply x by 9x^{6}-7x^{5}-4x^{3}-1.

$$5\left(-\left(9x^{7}-7x^{6}-4x^{4}-x\right)\right)$$

To find the opposite of 9x^{7}-7x^{6}-4x^{4}-x, find the opposite of each term.

$$5\left(-9x^{7}+7x^{6}+4x^{4}+x\right)$$

Use the distributive property to multiply 5 by -9x^{7}+7x^{6}+4x^{4}+x.

$$-45x^{7}+35x^{6}+20x^{4}+5x$$