Solve (3z^-4-6z^3-9z^2+3z-6)div(z+3)quad6

$$( 3 z ^ { - 4 } - 6 z ^ { 3 } - 9 z ^ { 2 } + 3 z - 6 ) \div ( z + 3 ) \quad 6$$

Evaluate

$$\frac{18\left(1-2z^{4}+z^{5}-3z^{6}-2z^{7}\right)}{\left(z+3\right)z^{4}}$$

Short Solution Steps

Express \frac{3z^{-4}-6z^{3}-9z^{2}+3z-6}{z+3}\times 6 as a single fraction.

$$\frac{\left(3z^{-4}-6z^{3}-9z^{2}+3z-6\right)\times 6}{z+3}$$

Use the distributive property to multiply 3z^{-4}-6z^{3}-9z^{2}+3z-6 by 6.

$$\frac{18z^{-4}-36z^{3}-54z^{2}+18z-36}{z+3}$$

Expand

$$-\frac{18\left(2z^{7}+3z^{6}-z^{5}+2z^{4}-1\right)}{\left(z+3\right)z^{4}}$$

Short Solution Steps

Express \frac{3z^{-4}-6z^{3}-9z^{2}+3z-6}{z+3}\times 6 as a single fraction.

$$\frac{\left(3z^{-4}-6z^{3}-9z^{2}+3z-6\right)\times 6}{z+3}$$

Use the distributive property to multiply 3z^{-4}-6z^{3}-9z^{2}+3z-6 by 6.

$$\frac{18z^{-4}-36z^{3}-54z^{2}+18z-36}{z+3}$$