Be the Professor Blog 4

Within today's lesson plan I will be explaining a key point that will follow you throughout the rest of your math careers: factoring.

Factoring for starters is actually rather simple to think about, but in practice can certain prove to be challenging when seen within complex equations. Understanding this, the easiest approach to the concept of factoring would be by starting with simple numbers, then moving on to simple equations and eventually making our way to more advanced ones.

So what exactly is a factor? It is easy to view a numbers factors as the terms that when multiplied together will give you the number that you seek. For example let us look at the number 12. The factors would be 1,12,2,6,3, and 4. Why? Because when you multiply 1*12, 2*6, and 3*4 they all will equal 12. It is also easy to view a factor as what numbers are the given number easily divisible by.

Just as single numbers can be factored, so too can variables with coefficients. In order to do this, the first step is to just find the factors of the coefficient. Knowing how to factor variables is useful for simplifying algebraic equations that the variables are among.

1. As an example the variable 12x can be written as the product of the two terms 12 and x. We then would write 12x as 3(4x) or 2(6x) ect. using which ever factors will best fit the problem that you are currently working on. 
2. You can even take the factoring one more step: look at 3(4x). You can then factory the coefficient 4 once more to produce: 3(2(2x)).

With the last two concepts it is finally time to take that knowledge of factoring both single numbers and variables with coefficients, you can move one more step to simplify algebraic equations by finding the factors that the numbers and variables in equation have in common. Usually to make the equation as simple as possible, we try to find the greatest common factor. This process is possible because of the distributive property of multiplication, which says that for any numbers a,b, and c, a(b+c)= ab+ac.

1. Let us look at an example problem. To factor the equation 12x6, first, find the greatest common factor of 12x and 6. 6 is the biggest number that divides evenly into both 12x and 6, so it can simplify the equation to 6(2x+1).

Now that you have a basic understanding of how to factor equations and numbers you should be able to tackle more and more complicated problems and they should not be as daunting. 

The only next step may be to factor a quadratic equation in order to so, it might be best to view this video and we will discuss it more in our next class: 

https://www.youtube.com/watch?v=ZQ-NRsWhOGI