ERROR ANALYSIS Describe and correct the error in factoring the polynomial completely. x x^4-4x^2+4=x^2(x^2-4)+4 =x^2(x+2)(x-2)+4

## Step 1<br />The given polynomial is \(x^{4}-4x^{2}+4\). The first step in factoring this polynomial is to identify the perfect square trinomial. A perfect square trinomial is a trinomial that can be factored into the square of a binomial. In this case, the trinomial is \(x^{4}-4x^{2}+4\), which can be factored into \((x^{2}-2)^{2}\).<br /><br />## Step 2<br />The next step is to factor the perfect square trinomial. The perfect square trinomial \((x^{2}-2)^{2}\) can be factored into \((x^{2}-2)(x^{2}-2)\).<br /><br />## Step 3<br />The final step is to factor the difference of squares. The difference of squares is a binomial of the form \(a^{2}-b^{2}\), which can be factored into \((a+b)(a-b)\). In this case, the difference of squares is \(x^{2}-2\), which can be factored into \((x+\sqrt{2})(x-\sqrt{2})\).