Problem

Find the roots of the function \( f(x) = x^3 - 6x^2 + 11x - 6 \) using the Factor Theorem.

Solution

Step 1 :Use the Factor Theorem to check possible roots, which are the factors of the constant term, -6. In this case, the possible roots are \(\pm 1\), \(\pm 2\), \(\pm 3\), and \(\pm 6\).

Step 2 :Check each possible root by substituting it into the function and seeing if it equals zero. We find that when \(x = 1\), \(x = 2\), and \(x = 3\), the function equals zero. Therefore, \(x = 1\), \(x = 2\), and \(x = 3\) are the roots of the function.

Step 3 :This means that the function can be factored as \(f(x) = (x - 1)(x - 2)(x - 3)\).

From Solvely APP
Source: https://solvelyapp.com/problems/S7tQM6ZXea/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download