blog #4 reggie

Good Evening class my name is Professor Boss, today I will be substituting for Professor Little and I will be teaching you the four ways of factoring.

Factoring is basically finding numbers that multiply so you solve an equation.

Simplifying- is a huge part of factoring. Simplifying is completely factoring an equation so there is no other possible solution.

Now that we have the general definitions for solving functions lets do a few simple practice problems.

Lets do an example:

1.x^2 – 6x + 9 

Step 1. Think of two “x” values that will add and get the value for the “x” term and that will multiply and get you the coefficient.

·      So since we are solving for numbers that multiple to get 6, the only factorable numbers are 1, 2, 3, 6. ( Hint- be careful with your signs. It is important to make sure your signs add up so you are getting the right expression. )

Step 2. Now that you know the numbers that factor lets choose the numbers that will make up this expression. What do you think? 1 and 6 do not work together, 2 and 3 do not work together, 3 and 6 do work together, but wait 3 and 3 may work.

Step 3.

If 3 and 3 work lets try to make an equation using those numbers. (Hint- always checks your signs!)

 So you have (x-3) (x-3)

Step 4. Explanation. The answer is (x-3) (x-3) because when you distribute you are left with +6 and -9.

There are two methods of factoring that I would like to teach you today. Factor by grouping and factoring by different of squares.

Factor by grouping is when you have an equation with four terms for example ( X^4-X^3+x^2-x) you factor by grouping when you have four terms and are able to find a common factor within two terms. By going that you are then left with two numbers left outside the parenthesis then combine those terms and put them in a separate parenthesis, and then solve for x.

Examples

Factor by grouping

1.     2x^4+x^- 2x^2-3x

2x^3(2x-3) 1 ( 2x-3)

(2x^3+1)( 2x-3) = 0

The second type of factoring I would like to teach you is factoring by differences of square.

To solve by using different of squares you need to have a perfect square (tend to come in the form of x^2 of x^4) and have a coefficient that is a whole number ( like 4, 9, 16, 25, 36, 49). Once you find that whole number you take the solution and you have one of the numbers added and the other multiplied. The who point of doing this is too eliminate the middle term and have a perfect square.

Examples

       1. x^2 - 16

(x-4) (x+4

2.     x^2-144

(x-12)(x+12)

I hope todays lesson helped you understand how factoring equations by factoring by grouping and using difference of squares. If you should have, but you shouldn’t because professor little is great, feel free to send me an email  at nicetrybutyoucanthavemyemail@american.edu. I hope I helped and have a nice day class.