Solve 12x^5+4x^4-60x^3-20x^2

$$12 x ^ { 5 } + 4 x ^ { 4 } - 60 x ^ { 3 } - 20 x ^ { 2 }$$

Factor

$$4\left(3x+1\right)x^{2}\left(x^{2}-5\right)$$

Solution Steps

Factor out 4.

$$4\left(3x^{5}+x^{4}-15x^{3}-5x^{2}\right)$$

Consider 3x^{5}+x^{4}-15x^{3}-5x^{2}. Factor out x^{2}.

$$x^{2}\left(3x^{3}+x^{2}-15x-5\right)$$

Consider 3x^{3}+x^{2}-15x-5. Do the grouping 3x^{3}+x^{2}-15x-5=\left(3x^{3}+x^{2}\right)+\left(-15x-5\right), and factor out x^{2} in the first and -5 in the second group.

$$x^{2}\left(3x+1\right)-5\left(3x+1\right)$$

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

$$\left(3x+1\right)\left(x^{2}-5\right)$$

Rewrite the complete factored expression. Polynomial x^{2}-5 is not factored since it does not have any rational roots.

$$4x^{2}\left(3x+1\right)\left(x^{2}-5\right)$$

Evaluate

$$4\left(3x+1\right)x^{2}\left(x^{2}-5\right)$$