Solve 3c^3-8c^2+2c-7+5c^3+2c^2+7

$$3 c ^ { 3 } - 8 c ^ { 2 } + 2 c - 7 + 5 c ^ { 3 } + 2 c ^ { 2 } + 7$$

Evaluate

$$2c\left(4c^{2}-3c+1\right)$$

Solution Steps

Combine 3c^{3} and 5c^{3} to get 8c^{3}.

$$8c^{3}-8c^{2}+2c-7+2c^{2}+7$$

Combine -8c^{2} and 2c^{2} to get -6c^{2}.

$$8c^{3}-6c^{2}+2c-7+7$$

Add -7 and 7 to get 0.

$$8c^{3}-6c^{2}+2c$$

Factor

$$2c\left(4c^{2}-3c+1\right)$$

Solution Steps

Multiply and combine like terms.

$$8c^{3}-6c^{2}+2c$$

Factor out 2.

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

Consider 4c^{3}-3c^{2}+c. Factor out c.

$$c\left(4c^{2}-3c+1\right)$$

Rewrite the complete factored expression. Polynomial 4c^{2}-3c+1 is not factored since it does not have any rational roots.

$$2c\left(4c^{2}-3c+1\right)$$