Solve 30x^4-41x^2y+14y^2

$$30 x ^ { 4 } - 41 x ^ { 2 } y + 14 y ^ { 2 }$$

Factor

$$\left(3x^{2}-2y\right)\left(10x^{2}-7y\right)$$

Solution Steps

Consider 30x^{4}-41x^{2}y+14y^{2} as a polynomial over variable x.

$$30x^{4}-41yx^{2}+14y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 30x^{4} and n divides the constant factor 14y^{2}. One such factor is 3x^{2}-2y. Factor the polynomial by dividing it by this factor.

$$\left(3x^{2}-2y\right)\left(10x^{2}-7y\right)$$

Evaluate

$$\left(3x^{2}-2y\right)\left(10x^{2}-7y\right)$$