Solve 12p^2-3pq-15q^2

$$12 p ^ { 2 } - 3 p q - 15 q ^ { 2 }$$

Factor

$$3\left(4p-5q\right)\left(p+q\right)$$

Solution Steps

Factor out 3.

$$3\left(4p^{2}-pq-5q^{2}\right)$$

Consider 4p^{2}-pq-5q^{2}. Consider 4p^{2}-pq-5q^{2} as a polynomial over variable p.

$$4p^{2}-qp-5q^{2}$$

Find one factor of the form kp^{m}+n, where kp^{m} divides the monomial with the highest power 4p^{2} and n divides the constant factor -5q^{2}. One such factor is 4p-5q. Factor the polynomial by dividing it by this factor.

$$\left(4p-5q\right)\left(p+q\right)$$

Rewrite the complete factored expression.

$$3\left(4p-5q\right)\left(p+q\right)$$

Evaluate

$$3\left(4p-5q\right)\left(p+q\right)$$