1. The problem: Understand and apply the Factor Theorem which states that for a polynomial $f(x)$, if $f(c)=0$ for some constant $c$, then $(x-c)$ is a factor of $f(x)$. 2. Step 1: Given a polynomial $f(x)$ and a value $c$, calculate $f(c)$. 3. Step 2: If $f(c)=0$, conclude by the Factor Theorem that $(x-c)$ divides $f(x)$ evenly. 4. Step 3: For example, if $f(x) = x^3 - 4x^2 + x + 6$ and $c=2$, evaluate $f(2) = 2^3 - 4(2)^2 + 2 + 6 = 8 - 16 + 2 + 6 = 0$, so $(x-2)$ is a factor of $f(x)$. 5. Step 4: Factor the polynomial further by polynomial division or synthetic division. 6. Thus, Factor Theorem helps find factors and roots of polynomials efficiently.