Solve x^2+x^4+x^2-8

$$x ^ { 2 } + x ^ { 4 } + x ^ { 2 } - 8$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$x^{4}+2x^{2}-8$$

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 -8. One such factor is x^{2}+4. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: x^{2}-2,x^{2}+4.

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

Evaluate

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

Solution Steps

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+x^{4}-8$$