Solve 21x^4+98x^3y-35x^2y^2

$$21 x ^ { 4 } + 98 x ^ { 3 } y - 35 x ^ { 2 } y ^ { 2 }$$

Factor

$$7\left(3x-y\right)\left(x+5y\right)x^{2}$$

Solution Steps

Factor out 7.

$$7\left(3x^{4}+14x^{3}y-5x^{2}y^{2}\right)$$

Consider 3x^{4}+14x^{3}y-5x^{2}y^{2}. Factor out x^{2}.

$$x^{2}\left(3x^{2}+14xy-5y^{2}\right)$$

Consider 3x^{2}+14xy-5y^{2}. Consider 3x^{2}+14xy-5y^{2} as a polynomial over variable x.

$$3x^{2}+14yx-5y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 3x^{2} and n divides the constant factor -5y^{2}. One such factor is 3x-y. Factor the polynomial by dividing it by this factor.

$$\left(3x-y\right)\left(x+5y\right)$$

Rewrite the complete factored expression.

$$7x^{2}\left(3x-y\right)\left(x+5y\right)$$

Evaluate

$$7\left(3x-y\right)\left(x+5y\right)x^{2}$$