Solve v^2+6vg+5g^2

$$v ^ { 2 } + 6 v g + 5 g ^ { 2 }$$

Factor

$$\left(v+g\right)\left(v+5g\right)$$

Solution Steps

Consider v^{2}+6vg+5g^{2} as a polynomial over variable v.

$$v^{2}+6gv+5g^{2}$$

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

$$\left(v+5g\right)\left(v+g\right)$$

Evaluate

$$\left(v+g\right)\left(v+5g\right)$$