Question 7 of 9, Step 1 of 4 Correct Consider the following polynomial function. \[ f(x)=x^{4}+x^{3}-4 x^{2}-2 x+4 \] Step 1 of 4 : Factor the polynomial completely. Answer \[ f(x)= \]

Step 1 ：Consider the polynomial function \(f(x)=x^{4}+x^{3}-4 x^{2}-2 x+4\).

Step 2 ：To factor the polynomial completely, we need to find the roots of the polynomial. The roots of the polynomial are the values of x for which \(f(x) = 0\).

Step 3 ：The roots of the polynomial are -2, -1.41421356, 1.41421356, and 1. These are the values of x for which \(f(x) = 0\). We can use these roots to factor the polynomial.

Step 4 ：The factored form of a polynomial is the product of terms \((x - root)\), where each root is a root of the polynomial. Therefore, the factored form of the polynomial is \(f(x) = (x - (-2))(x - (-1.41421356))(x - 1.41421356)(x - 1)\).

Step 5 ：We can simplify this to: \(f(x) = (x + 2)(x + 1.41421356)(x - 1.41421356)(x - 1)\).

Step 6 ：\(\boxed{f(x) = (x + 2)(x + 1.41421356)(x - 1.41421356)(x - 1)}\)