Solve 3x^2+3x^5

$$3 { x }^{ 2 } +3 { x }^{ 5 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(x^{2}+x^{5}\right)$$

Consider x^{2}+x^{5}. Factor out x^{2}.

$$x^{2}\left(1+x^{3}\right)$$

Consider 1+x^{3}. Rewrite 1+x^{3} 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.

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

Evaluate

$$3x^{2}\left(x^{3}+1\right)$$