This week we started to practice and look at the tactics we can use to make factoring easier. Here I will be talking about factoring from a question like (x²+x+1) and turning it into (x+1)(x+1).

Using an example like (x²+7x+12) you would start by looking at the signs to see if they are negative or positive. Knowing that they are all positive you can now see that it is a trinomial. So, the new equation would have to look like this (x+?)(x+?). Also, knowing that there is only an x at the beginning of each bracket because, in the example, there is only a one as a coefficient to “x².”

After you have found the layout of your new equation, you need to find two numbers that will multiply into 12 and add into 7. If there is a coefficient larger than one attached to the x², you would want to find the product. This means multiplying the “x²” coefficient and the number. In this equation, there is no need.

To find the numbers for the new equation, you must look at everything that multiplies into the number (12). These being; 1×12, 2×6, and 3×4.

Then, you must find the pair of numbers equal to 7 if you add them together. In this case, the number would be 3 and 4. Using this information, your new equation would be (x+3)(x+4).

If you want to move the other way and start with an equation like (x+5)(x+6), you need to use the FOIL method. Multiply the X’s together to create x², continue the FOIL method till you reach x²+6x+5x+30. Simplify the equation, adding the two X’s together to create the equation of x²+11x+30