Solve 3ax^2-6x^2+3a-6

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

Factor

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

Solution Steps

Factor out 3.

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

Consider ax^{2}-2x^{2}+a-2. Do the grouping ax^{2}-2x^{2}+a-2=\left(ax^{2}-2x^{2}\right)+\left(a-2\right), and factor out x^{2} in ax^{2}-2x^{2}.

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

Factor out common term a-2 by using distributive property.

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

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

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

Evaluate

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