Question 4 Find all zeros of f(x)=x^3-10x^2+30x-24 Enter the zeros separated by commas. Enter exact value, not decimal approximations. square Question Help: Video (1) Message instructor

To find the zeros of the polynomial function \( f(x) = x^3 - 10x^2 + 30x - 24 \), we need to solve the equation \( f(x) = 0 \).First, we can try to find rational roots using the Rational Root Theorem, which states that any rational root of the polynomial \( f(x) \) is a factor of the constant term (-24) divided by a factor of the leading coefficient (1). Therefore, the possible rational roots are: We can test these possible roots by substituting them into the polynomial to see if they yield zero.Let's start with : So, is not a root.Next, let's try : So, is not a root.Next, let's try : So, is not a root.Next, let's try : So, is a root.Now that we have found one root, we can use polynomial division to factor the polynomial and find the other roots. We divide \( f(x) \) by \( (x - 4) \):Using synthetic division or long division, we get: Now, we need to solve the quadratic equation to find the remaining roots. We can use the quadratic formula: where , , and .Substituting these values into the formula, we get: So, the zeros of the polynomial \( f(x) = x^3 - 10x^2 + 30x - 24 \) are: