Solve 4x^4+24x^2y^5-85y^10

$$4 x ^ { 4 } + 24 x ^ { 2 } y ^ { 5 } - 85 y ^ { 10 }$$

Factor

$$\left(2x^{2}-5y^{5}\right)\left(2x^{2}+17y^{5}\right)$$

Solution Steps

Consider 4x^{4}+24x^{2}y^{5}-85y^{10} as a polynomial over variable x.

$$4x^{4}+24y^{5}x^{2}-85y^{10}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 4x^{4} and n divides the constant factor -85y^{10}. One such factor is 2x^{2}+17y^{5}. Factor the polynomial by dividing it by this factor.

$$\left(2x^{2}+17y^{5}\right)\left(2x^{2}-5y^{5}\right)$$

Evaluate

$$4x^{4}+24x^{2}y^{5}-85y^{10}$$