Solve 6p^2+pq-15q^2

$$6 p ^ { 2 } + p q - 15 q ^ { 2 }$$

Factor

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

Solution Steps

Consider 6p^{2}+pq-15q^{2} as a polynomial over variable p.

$$6p^{2}+qp-15q^{2}$$

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 -15q^{2}. One such factor is 2p-3q. Factor the polynomial by dividing it by this factor.

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

Evaluate

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