Solve {c}{pq^2-5q^2}{+p^2-10p}{+25}

$$\left. \begin{array} { c } { p q ^ { 2 } - 5 q ^ { 2 } } \\ { + p ^ { 2 } - 10 p } \\ { + 25 } \end{array} \right.$$

Factor

$$\left(p-5\right)\left(p+q^{2}-5\right)$$

Solution Steps

Consider pq^{2}-5q^{2}+p^{2}-10p+25 as a polynomial over variable p.

$$p^{2}+\left(q^{2}-10\right)p-5q^{2}+25$$

Find one factor of the form p^{k}+m, where p^{k} divides the monomial with the highest power p^{2} and m divides the constant factor -5q^{2}+25. One such factor is p-5. Factor the polynomial by dividing it by this factor.

$$\left(p-5\right)\left(p+q^{2}-5\right)$$

Evaluate

$$\left(p-5\right)\left(p+q^{2}-5\right)$$