Solve 4x^{3}+3x^{2}-3x-2x^{3}+12x^{2}+x^5-8x^3+3x^2-x^5=

$$4 x ^ { 3 } + 3 x ^ { 2 } - 3 x - 2 x ^ { 3 } + 12 x ^ { 2 } + x ^ { 5 } - 8 x ^ { 3 } + 3 x ^ { 2 } - x ^ { 5 } =$$

Evaluate

$$3x\left(-2x^{2}+6x-1\right)$$

Solution Steps

Combine 4x^{3} and -2x^{3} to get 2x^{3}.

$$2x^{3}+3x^{2}-3x+12x^{2}+x^{5}-8x^{3}+3x^{2}-x^{5}$$

Combine 3x^{2} and 12x^{2} to get 15x^{2}.

$$2x^{3}+15x^{2}-3x+x^{5}-8x^{3}+3x^{2}-x^{5}$$

Combine 2x^{3} and -8x^{3} to get -6x^{3}.

$$-6x^{3}+15x^{2}-3x+x^{5}+3x^{2}-x^{5}$$

Combine 15x^{2} and 3x^{2} to get 18x^{2}.

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

Combine x^{5} and -x^{5} to get 0.

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

Factor

$$-6x\left(x-\frac{3-\sqrt{7}}{2}\right)\left(x-\frac{\sqrt{7}+3}{2}\right)$$