The processes are described in plain English (as close to plain English as we get in math). To see the the process written out in proper form, watch the video.

• Remember that factoring is extremely challenging so practice every chance you get.

• Common factoring means seeing something which can divide into all of the terms of an expression and pulling it out to the front, in front of a bracket. This is the distributive property done backwards.

• You can always check to see if you factored correctly by using the distributive property to see if you get exactly what you started with.

• Remember that not all expressions factor, so after you have tried every way you know of factoring and nothing has worked, you write N.F. for “not factorable.”

• Factoring trinomials. There are two cases: easy and hard. Easy comes when there is no coefficient in front of the x-squared term. Hard means there is.

• For the easy case, look at the last term, then make a list of all the ways to form that term by multiplication (e.g. 12: 1x12, 2x6, 3x4). Find one of the pairs which can be added together (or subtracted) to make the middle coefficient. If the sign of the last number is positive, it means you need to choose two numbers with the same sign. If the sign of the last term is negative, you need to take two numbers of opposite sign. The trinomial factors into two brackets, x plus the first number, x plus the second number.

• For the hard case: Multiply together the first and last coefficients. Similar to before, take the result and make the complete list of all the ways to form this number by multiplication. Look at the middle term of the trinomial, find two numbers from your list which can be added (or subtracted together to get the middle term.) Now the process changes from above. Split the middle term using the numbers you just found. Take each half separately and common factor each half. Done properly, you now have two brackets which should be identical. Factor out this bracket which leaves you with the two separate brackets you were looking for.

• For both cases of trinomial, if you make the list of ways to form the number by multiplication and try every combination to see if you can form the middle term and none of them work it means that this trinomial does not factor.

• Difference of Squares refers to two perfect squares separated by a minus sign. Those always factor as two brackets which are nearly the same. Each bracket starts with the square root of the first term, the the square root of the second term. One bracket receives a plus sign, the other gets a minus sign.