Solve p-q^2+pq^2-1

$$p - q ^ { 2 } + p q ^ { 2 } - 1$$

Factor

$$\left(p-1\right)\left(q^{2}+1\right)$$

Solution Steps

Do the grouping p-q^{2}+pq^{2}-1=\left(pq^{2}+p\right)+\left(-q^{2}-1\right), and factor out p in the first and -1 in the second group.

$$p\left(q^{2}+1\right)-\left(q^{2}+1\right)$$

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

$$\left(q^{2}+1\right)\left(p-1\right)$$

Evaluate

$$\left(p-1\right)\left(q^{2}+1\right)$$