Solve 14c^3-42c^5div49c^4

$$14 c ^ { 3 } - 42 c ^ { 5 } \div 49 c ^ { 4 }$$

Evaluate

$$-\frac{6c^{9}}{7}+14c^{3}$$

Solution Steps

Divide 42c^{5} by 49 to get \frac{6}{7}c^{5}.

$$14c^{3}-\frac{6}{7}c^{5}c^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$14c^{3}-\frac{6}{7}c^{9}$$

Factor

$$\frac{2c^{3}\left(49-3c^{6}\right)}{7}$$

Solution Steps

Factor out \frac{2}{7}.

$$\frac{2\left(49c^{3}-3c^{5}c^{4}\right)}{7}$$

Consider 49c^{3}-3c^{9}. Factor out c^{3}.

$$c^{3}\left(49-3c^{6}\right)$$

Rewrite the complete factored expression. Polynomial 49-3c^{6} is not factored since it does not have any rational roots.

$$\frac{2c^{3}\left(49-3c^{6}\right)}{7}$$