Solve px^2-11pxy+24py^2

$$p x ^ { 2 } - 11 p x y + 24 p y ^ { 2 }$$

Factor

$$p\left(x-3y\right)\left(x-8y\right)$$

Solution Steps

Factor out p.

$$p\left(x^{2}-11xy+24y^{2}\right)$$

Consider x^{2}-11xy+24y^{2}. Consider x^{2}-11xy+24y^{2} as a polynomial over variable x.

$$x^{2}-11yx+24y^{2}$$

Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor 24y^{2}. One such factor is x-8y. Factor the polynomial by dividing it by this factor.

$$\left(x-8y\right)\left(x-3y\right)$$

Rewrite the complete factored expression.

$$p\left(x-8y\right)\left(x-3y\right)$$

Evaluate

$$p\left(x-3y\right)\left(x-8y\right)$$