1. The problem is to understand and apply the Factor and Remainder Theorem. 2. The Factor Theorem states that if a polynomial $f(x)$ is divided by $(x - a)$, then the remainder is $f(a)$. If $f(a) = 0$, then $(x - a)$ is a factor of $f(x)$. 3. To use the theorem, substitute $x = a$ into the polynomial and evaluate $f(a)$. 4. If $f(a) = 0$, conclude that $(x - a)$ is a factor. 5. If $f(a) \neq 0$, the remainder is $f(a)$. 6. Example: For $f(x) = x^3 - 4x^2 + x + 6$, check if $(x - 2)$ is a factor. 7. Calculate $f(2) = 2^3 - 4(2)^2 + 2 + 6 = 8 - 16 + 2 + 6 = 0$. 8. Since $f(2) = 0$, $(x - 2)$ is a factor of $f(x)$. 9. This theorem helps factor polynomials and find roots efficiently.