Solve 6x^5+2x^4-18x^3-6x^2

$$6 x ^ { 5 } + 2 x ^ { 4 } - 18 x ^ { 3 } - 6 x ^ { 2 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(3x^{5}+x^{4}-9x^{3}-3x^{2}\right)$$

Consider 3x^{5}+x^{4}-9x^{3}-3x^{2}. Factor out x^{2}.

$$x^{2}\left(3x^{3}+x^{2}-9x-3\right)$$

Consider 3x^{3}+x^{2}-9x-3. Do the grouping 3x^{3}+x^{2}-9x-3=\left(3x^{3}+x^{2}\right)+\left(-9x-3\right), and factor out x^{2} in the first and -3 in the second group.

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

Factor out common term 3x+1 by using distributive property.

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

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

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

Evaluate

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