Solve 9p^2-45pq-126q^2

$$9 p ^ { 2 } - 45 p q - 126 q ^ { 2 }$$

Factor

$$9\left(p-7q\right)\left(p+2q\right)$$

Solution Steps

Factor out 9.

$$9\left(p^{2}-5pq-14q^{2}\right)$$

Consider p^{2}-5pq-14q^{2}. Consider p^{2}-5pq-14q^{2} as a polynomial over variable p.

$$p^{2}-5qp-14q^{2}$$

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 -14q^{2}. One such factor is p-7q. Factor the polynomial by dividing it by this factor.

$$\left(p-7q\right)\left(p+2q\right)$$

Rewrite the complete factored expression.

$$9\left(p-7q\right)\left(p+2q\right)$$

Evaluate

$$9\left(p-7q\right)\left(p+2q\right)$$