Solve 3p^2+13pq+4q^2

$$3 p ^ { 2 } + 13 p q + 4 q ^ { 2 }$$

Factor

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

Solution Steps

Consider 3p^{2}+13pq+4q^{2} as a polynomial over variable p.

$$3p^{2}+13qp+4q^{2}$$

Find one factor of the form kp^{m}+n, where kp^{m} divides the monomial with the highest power 3p^{2} and n divides the constant factor 4q^{2}. One such factor is 3p+q. Factor the polynomial by dividing it by this factor.

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

Evaluate

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