Solve 6p^2-7pq-5q^2

$$6 p ^ { 2 } - 7 p q - 5 q ^ { 2 }$$

Factor

$$\left(3p-5q\right)\left(2p+q\right)$$

Solution Steps

Consider 6p^{2}-7pq-5q^{2} as a polynomial over variable p.

$$6p^{2}-7qp-5q^{2}$$

Find one factor of the form kp^{m}+n, where kp^{m} divides the monomial with the highest power 6p^{2} and n divides the constant factor -5q^{2}. One such factor is 2p+q. Factor the polynomial by dividing it by this factor.

$$\left(2p+q\right)\left(3p-5q\right)$$

Evaluate

$$\left(3p-5q\right)\left(2p+q\right)$$