Solve 2x^4-20x^2+42

$$2 x ^ { 4 } - 20 x ^ { 2 } + 42$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(x^{4}-10x^{2}+21\right)$$

Consider x^{4}-10x^{2}+21. Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{4} and m divides the constant factor 21. One such factor is x^{2}-7. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: x^{2}-7,x^{2}-3.

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

Evaluate

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