Solve 12p^4+61p^3q+5p^2q^2

$$12 p ^ { 4 } + 61 p ^ { 3 } q + 5 p ^ { 2 } q ^ { 2 }$$

Factor

$$\left(p+5q\right)\left(12p+q\right)p^{2}$$

Solution Steps

Factor out p^{2}.

$$p^{2}\left(12p^{2}+61pq+5q^{2}\right)$$

Consider 12p^{2}+61pq+5q^{2}. Consider 12p^{2}+61pq+5q^{2} as a polynomial over variable p.

$$12p^{2}+61qp+5q^{2}$$

Find one factor of the form kp^{m}+n, where kp^{m} divides the monomial with the highest power 12p^{2} and n divides the constant factor 5q^{2}. One such factor is 12p+q. Factor the polynomial by dividing it by this factor.

$$\left(12p+q\right)\left(p+5q\right)$$

Rewrite the complete factored expression.

$$p^{2}\left(12p+q\right)\left(p+5q\right)$$

Evaluate

$$\left(p+5q\right)\left(12p+q\right)p^{2}$$