Solve x^4+4x^2+x^2+4

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

Factor

$$\left(x^{2}+1\right)\left(x^{2}+4\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{4}+5x^{2}+4$$

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 4. 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}+1,x^{2}+4.

$$\left(x^{2}+4\right)\left(x^{2}+1\right)$$

Evaluate

$$\left(x^{2}+1\right)\left(x^{2}+4\right)$$

Solution Steps

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$x^{4}+5x^{2}+4$$