Solve a^3x^2-ax-4a^3-2a

$$a ^ { 3 } x ^ { 2 } - a x - 4 a ^ { 3 } - 2 a$$

Factor

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

Solution Steps

Factor out a.

$$a\left(a^{2}x^{2}-x-4a^{2}-2\right)$$

Consider a^{2}x^{2}-x-4a^{2}-2. Consider a^{2}x^{2}-x-4a^{2}-2 as a polynomial over variable x.

$$a^{2}x^{2}-x-4a^{2}-2$$

Find one factor of the form a^{k}x^{m}+n, where a^{k}x^{m} divides the monomial with the highest power a^{2}x^{2} and n divides the constant factor -4a^{2}-2. One such factor is x+2. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression.

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

Evaluate

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