Solve 10s^2+st-2t^2

$$10 s ^ { 2 } + s t - 2 t ^ { 2 }$$

Factor

$$\left(5s-2t\right)\left(2s+t\right)$$

Solution Steps

Consider 10s^{2}+st-2t^{2} as a polynomial over variable s.

$$10s^{2}+ts-2t^{2}$$

Find one factor of the form ks^{m}+n, where ks^{m} divides the monomial with the highest power 10s^{2} and n divides the constant factor -2t^{2}. One such factor is 2s+t. Factor the polynomial by dividing it by this factor.

$$\left(2s+t\right)\left(5s-2t\right)$$

Evaluate

$$\left(5s-2t\right)\left(2s+t\right)$$