The AC method is a useful way to factor trinomials that look like $ax^2 + bx + c$. This method makes factoring easier and quicker. Let's go through it step-by-step.

Step 1: Identify $a$, $b$, and $c$

First, you need to find the numbers in your trinomial. For example, in $6x^2 + 11x + 3$, we can see:

• $a = 6$
• $b = 11$
• $c = 3$

Step 2: Calculate $ac$

Next, multiply $a$ and $c$. In our case, $ac$ is: $6 \times 3 = 18$

Step 3: Find Two Numbers

Now, you need to find two numbers that multiply to $ac$ (which is 18) and add up to $b$ (which is 11). The numbers 9 and 2 work because:

• $9 \times 2 = 18$
• $9 + 2 = 11$

Step 4: Rewrite the Middle Term

Now, we can rewrite the trinomial using these two numbers to break up the middle term: $6x^2 + 9x + 2x + 3$

Step 5: Factor by Grouping

Next, group the terms together: $(6x^2 + 9x) + (2x + 3)$

Now, factor out the common factors from each group: $3x(2x + 3) + 1(2x + 3)$

You’ll notice that we have a common binomial: $(3x + 1)(2x + 3)$

Conclusion

And that's it! The factored form of $6x^2 + 11x + 3$ is $(3x + 1)(2x + 3)$. By using the AC method, you can simplify factoring and tackle more complicated trinomials with ease. Give it a shot with other trinomials, and you’ll see how effective this method is!