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

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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)).

Answer

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)).

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

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