In factoring by the ac method, which is the final step?

• A. Identify a, b, c
• B. Set up giant X with ac in the top and b in the bottom
• C. Find factors that multiply to ac but add to b
• D. Divide factors by a and simplify

Answer: (D)

In factoring by the ac method, you’re turning ax^2 + bx + c into a product of two binomials by splitting the middle term using ac and then factoring by grouping. After you’ve found two numbers that multiply to ac and add to b and you’ve rewritten and factored, the final move is to simplify the factors by dividing out any extra factor of a that may have appeared, so the two binomial factors multiply to the original trinomial with the correct leading coefficient a. Often this last step isn’t needed, but when an a-factor shows up in the factors, dividing by a cleans things up and gives the standard, simplest factorization.