1. The problem is to factor a given polynomial expression using the factor method. 2. First, identify the polynomial that needs to be factored. Since no specific polynomial is provided, let's consider an example: $x^2 + 5x + 6$. 3. To factor $x^2 + 5x + 6$, find two numbers that multiply to the constant term $6$ and add up to the middle coefficient $5$. 4. The numbers are $2$ and $3$ because $2 \times 3 = 6$ and $2 + 3 = 5$. 5. Rewrite the middle term $5x$ as $2x + 3x$: $$x^2 + 2x + 3x + 6.$$ 6. Group terms: $$(x^2 + 2x) + (3x + 6).$$ 7. Factor out the common factor from each group: $$x(x + 2) + 3(x + 2).$$ 8. Factor out the common binomial factor $(x + 2)$: $$(x + 2)(x + 3).$$ 9. The factored form of $x^2 + 5x + 6$ is $$(x + 2)(x + 3).$$ 10. This method can be applied to any quadratic polynomial where the leading coefficient is 1.