Consider the following polynomial function.
\[
f(x)=x^{4}-4 x^{3}-8 x^{2}+12 x+15
\]
Step 1 of 4 : Factor the polynomial completely.
Answer
\[
f(x)=
\]
Answer
\(\boxed{The factorized form of the polynomial is (x - 5)(x + 1)(x - \sqrt{3})(x + \sqrt{3})}\)
Step 1 ：Consider the following polynomial function: \(f(x)=x^{4}-4 x^{3}-8 x^{2}+12 x+15\)
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 \(f(x) = 0\). We can find the roots by setting the polynomial equal to zero and solving for x.
Step 3 ：The roots of the polynomial are -1, 5, -\(\sqrt{3}\), and \(\sqrt{3}\). We can use these roots to factor the polynomial.
Step 4 ：\(\boxed{The factorized form of the polynomial is (x - 5)(x + 1)(x - \sqrt{3})(x + \sqrt{3})}\)
