Final answer:
To find all the zeros of the function f(x) = x^3 - 5x^2 - 4x + 20 using factoring, we need to factorize the function and solve for x when f(x) equals zero.
Step-by-step explanation:
To find all the zeros of the function f(x) = x^3 - 5x^2 - 4x + 20 using factoring, we need to factorize the function and solve for x when f(x) equals zero.
Step 1: Write the function in factored form.
f(x) = (x - a)(x - b)(x - c)
where a, b, and c are the zeros.
Step 2: Equate f(x) to zero.
(x - a)(x - b)(x - c) = 0
Step 3: Solve for x by setting each factor equal to zero.
x - a = 0, x - b = 0, x - c = 0
Step 4: Solve for a, b, and c by finding the values of x that make each factor equal to zero.
Therefore, to find all the zeros of the given function, we need to factorize it and solve for x by setting each factor equal to zero.