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

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

Factor

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

Solution Steps

Factor out a.

$$a\left(x^{4}-3x^{2}-4\right)$$

Consider x^{4}-3x^{2}-4. Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{4} and m divides the constant factor -4. One such factor is x^{2}-4. Factor the polynomial by dividing it by this factor.

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

Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(x-2\right)\left(x+2\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+1 is not factored since it does not have any rational roots.

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

Evaluate

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