Solve x^3+5x^3+6

$${ x }^{ 3 } +5 { x }^{ 3 } +6$$

Factor

$$6\left(x+1\right)\left(x^{2}-x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$6x^{3}+6$$

Factor out 6.

$$6\left(x^{3}+1\right)$$

Consider x^{3}+1. Rewrite x^{3}+1 as x^{3}+1^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(x+1\right)\left(x^{2}-x+1\right)$$

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

$$6\left(x+1\right)\left(x^{2}-x+1\right)$$

Evaluate

$$6\left(x^{3}+1\right)$$

Solution Steps

Combine x^{3} and 5x^{3} to get 6x^{3}.

$$6x^{3}+6$$