Solve (3q^5-12q^3+6q^2)div6q^2

$$( 3 q ^ { 5 } - 12 q ^ { 3 } + 6 q ^ { 2 } ) \div 6 q ^ { 2 }$$

Evaluate

$$\frac{\left(q^{3}-4q+2\right)q^{4}}{2}$$

Solution Steps

Express \frac{3q^{5}-12q^{3}+6q^{2}}{6}q^{2} as a single fraction.

$$\frac{\left(3q^{5}-12q^{3}+6q^{2}\right)q^{2}}{6}$$

Use the distributive property to multiply 3q^{5}-12q^{3}+6q^{2} by q^{2}.

$$\frac{3q^{7}-12q^{5}+6q^{4}}{6}$$

Expand

$$\frac{q^{7}}{2}-2q^{5}+q^{4}$$

Solution Steps

Express \frac{3q^{5}-12q^{3}+6q^{2}}{6}q^{2} as a single fraction.

$$\frac{\left(3q^{5}-12q^{3}+6q^{2}\right)q^{2}}{6}$$

Use the distributive property to multiply 3q^{5}-12q^{3}+6q^{2} by q^{2}.

$$\frac{3q^{7}-12q^{5}+6q^{4}}{6}$$