Section 3.5 HW Score: 3/6 Answered: 4/6 Question 5 Find all zeros of f(x)=x^3-x^2-18x-10 Enter the zeros separated by commas. Enter exact value, not decimal approximations. square Question Help: El Video B Message instructor

To find the zeros of the polynomial function \( f(x) = x^3 - x^2 - 18x - 10 \), we need to solve for such that \( f(x) = 0 \).First, we can use the Rational Root Theorem to identify possible rational roots. The Rational Root Theorem states that any rational root of the polynomial \( f(x) \) is a factor of the constant term divided by a factor of the leading coefficient.For \( f(x) = x^3 - x^2 - 18x - 10 \):- The constant term is .- The leading coefficient is .The factors of are .We will 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 not.Next, let's try : So, is a root.Now that we have found one root, , we can use polynomial division or synthetic division to factor the polynomial and find the other roots.We can factor \( f(x) \) as: Now, we need to solve the quadratic equation using the quadratic formula: where , , and . So, the zeros of \( f(x) = x^3 - x^2 - 18x - 10 \) are: Therefore, the exact values of the zeros are: