This week we learned how to use the box method to factor trinomials that didn’t have a leading coefficient of 1 (ugly trinomials). For me, the box method is nice because it doesn’t require me to do as much thinking in my head as the inspection method.

As an example, if you have the expression these are the steps to factor it.

1. Draw a box and split it into quarters so that there are four spaces inside.

2. Write the first term () in the top left-hand corner and write the last term (10) in the bottom right-hand corner.

3. Multiply the two numbers without the variable (30) and find the factors of that number that add up to the middle term (11).

4. Look which numbers already inside the box have corresponding factors or things in common and place them in the two leftover spots. After, add in the variable to the numbers.

5. Find out which numbers multiply to get the numbers in the box and put them on the outside spaces accordingly. It works like a multiplication table.

6. Once you’re done, write the answer in parentheses (3x+5)(x+2)