1. The problem is to use the Factor Theorem to determine if a given binomial is a factor of a polynomial or to factorize the polynomial. 2. The Factor Theorem states that if $f(c) = 0$ for a polynomial $f(x)$, then $(x - c)$ is a factor of $f(x)$. 3. To apply the Factor Theorem, substitute $x = c$ into the polynomial and evaluate. 4. If the result is zero, then $(x - c)$ is a factor; otherwise, it is not. 5. For example, if we want to check if $(x - 2)$ is a factor of $f(x) = x^3 - 4x^2 + x + 6$, we calculate $f(2) = 2^3 - 4(2)^2 + 2 + 6 = 8 - 16 + 2 + 6 = 0$. 6. Since $f(2) = 0$, $(x - 2)$ is a factor of $f(x)$. 7. Then, divide $f(x)$ by $(x - 2)$ to find the other factors or quotient polynomial. 8. Use polynomial division or synthetic division to divide $f(x)$ by $(x - 2)$. 9. The quotient is $x^2 - 2x - 3$, which can be factored further as $(x - 3)(x + 1)$. 10. Therefore, the complete factorization of $f(x)$ is $(x - 2)(x - 3)(x + 1)$. This method helps to factorize polynomials by testing possible roots and confirming factors using the Factor Theorem.