Solve x^2+ax^2+x+ax-1-a

$$x ^ { 2 } + a x ^ { 2 } + x + a x - 1 - a$$

Factor

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

Solution Steps

Do the grouping x^{2}+ax^{2}+x+ax-1-a=\left(x^{2}+ax^{2}\right)+\left(x+ax\right)+\left(-1-a\right), and factor out x^{2},x,-1 in each of the groups respectively.

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

Factor out common term a+1 by using distributive property. Polynomial x^{2}+x-1 is not factored since it does not have any rational roots.

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

Evaluate

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