Question

Question 6

on f(x) = x³ - 11x² + 36x - 36 has x = 3 as a root.
what are the remaining roots of f(x)? Separate multiple answers with a comma.

Answer 1

To find the remaining roots of the polynomial function f(x) = x³ - 11x² + 36x - 36, divide the polynomial by (x - 3) using synthetic division. Factor the resulting quadratic equation to find the remaining roots x = 2 and x = 6.

Step-by-step explanation:

To find the remaining roots of the polynomial function f(x) = x³ - 11x² + 36x - 36, we can use synthetic division or factoring.

Since the given value x = 3 is a root of the equation, we can use synthetic division to divide the polynomial by (x - 3).

This will give us a quadratic equation which we can solve to find the remaining roots:

x³ - 11x² + 36x - 36 ÷ (x - 3) = x² - 8x + 12

Now, we can factor the quadratic equation x² - 8x + 12 to find the remaining roots:

(x - 2)(x - 6)

Therefore, the remaining roots of f(x) = x³ - 11x² + 36x - 36 are x = 2 and x = 6.