Solve 2r^2t-9rst+10s^2t

$$2 r ^ { 2 } t - 9 r s t + 10 s ^ { 2 } t$$

Factor

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

Solution Steps

Factor out t.

$$t\left(2r^{2}-9rs+10s^{2}\right)$$

Consider 2r^{2}-9rs+10s^{2}. Consider 2r^{2}-9rs+10s^{2} as a polynomial over variable r.

$$2r^{2}-9sr+10s^{2}$$

Find one factor of the form kr^{m}+n, where kr^{m} divides the monomial with the highest power 2r^{2} and n divides the constant factor 10s^{2}. One such factor is 2r-5s. Factor the polynomial by dividing it by this factor.

$$\left(2r-5s\right)\left(r-2s\right)$$

Rewrite the complete factored expression.

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

Evaluate

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