1. **Problem Statement:** Factor the polynomial using the Remainder Theorem. 2. **Remainder Theorem:** If a polynomial $f(x)$ is divided by $(x - a)$, the remainder is $f(a)$. 3. **Using the Theorem:** To check if $(x - a)$ is a factor of $f(x)$, evaluate $f(a)$. If $f(a) = 0$, then $(x - a)$ is a factor. 4. **Example:** Suppose $f(x) = x^3 - 4x^2 + x + 6$. To check if $(x - 2)$ is a factor, calculate $f(2) = 2^3 - 4(2)^2 + 2 + 6 = 8 - 16 + 2 + 6 = 0$. 5. Since $f(2) = 0$, $(x - 2)$ is a factor. 6. **Factorization:** Use polynomial division or synthetic division to divide $f(x)$ by $(x - 2)$ to find the other factors. 7. Dividing, we get $f(x) = (x - 2)(x^2 - 2x - 3)$. 8. Factor the quadratic: $x^2 - 2x - 3 = (x - 3)(x + 1)$. 9. **Final factorization:** $$f(x) = (x - 2)(x - 3)(x + 1)$$ This shows how the Remainder Theorem helps identify factors and factor polynomials completely.