FACTORING


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FACTORING (PULL OUT METHOD)**

The Strategy of the Pull Out Method is to find the GCF and place it in front of the parenthesis leaving what's left behind in the parenthesis. With that said, this is how the pull out method works.

Example 1: (30 + 45) The first step is to observe and try to find the GCF of your problem. (30 + 45)

Now we need to find the GCF of the problem. 15 x 2= 30 15 x 3= 45

As you can see, 15 is the GCF because it can be multiplied by both numbers. This also means that 15 is the number that will be pulled out of the parenthesis and placed in the front of them. 15 will still be multiplied by both numbers just in a simpler form. 15(2+3)

And that’s the process. Let’s try another!

Example 2: (5y^3 + 10y^2x) There is a y^3 and a y^2. these mean the there are 3 y’s and 2 y’s. In other words, they are exponents. This means the problem needs to be written out. When variables are involved, you ALWAYS write out the problem to make sure you are correct. (5yyy + 10yyx)

Now that we have written out the problem, we need to find the GCF of 5 and 10. We all know that 5 x 2= 10 which means the GCF is 5. (5yyy + 5 x 2yyx)

As you can see, both sides have two things in common. You already know there are two 5's which means they need to be circled and placed out of the parenthesis. There are 3 y's on one side of the problem and 2 on the other. Since both sides have 2 y's, they need to be circled and placed out of the parenthesis also. They have to go behind the 5 because letters always go behind numbers. 5yy(y + 2x)

I was left with a y and a 2x in the parenthesis because there was a 5 and 3 y's but two left which left me with a y. On the other side, there was a 5, a 2, and 2 y's but the 5 and the 2 y's left which left me with a 2 and a x. Now we need to simplify the equation. 5y^2(y + 2x)

Example 3: 12x^2y + 6x^3 - 4x^2y^3 Our first step is to observe and find the GCF.

2 is the largest number that can be multiplied by 12, 6, and 4 so 2 has to be taken out. 6 x 2xxy + 3 x 2xxx - 2 x 2xxyyy

All the sides have at least 2 x's so they have to be taken out also. 2xx(6y + 3x - 2yyy)

Now we have to simplify the problem. 2x^2(6y + 3x - 2y^3)

When you find the difference of two squares, you look for each number's square root. Example: x²+16 x times x equals x² and 4 times 4 equals 16. Therefore, you would write your answer as: (x+4) (x-4).** [|Math Is Fun - Maths Resources]" class="wiki_link_ext">math!!!! [|**difference of 2 squares**]
 * FACTORING (DIFFERENCE OF 2 SQUARES)

the quadratic equation: x=(-b±√b^2-4ac)/2a**  Step 1: Find values for variables a,b,c A=1 B=7 C=5 Step 2: replace variables with values x=(-7±√7²-4(1)(5))÷2(1) Step 3: Order of operations x=[-7±√49-4(1)(5)] ÷2(1) Parenthesis exponents
 * FACTORING QUADRATICS:
 * Example 1 1X²+7X+5

x=(-7±√49-20)÷2(1) _Parenthesis multiply

x=(-7±√29 )÷2(1) _Parenthesis subtraction

-7+√29**≈5.4 _Parenthesis addition

2(1)=2 _Multiplication

Answer is 2.7
 * 5.4÷2 _Division**

Answer is≈2.7(1st zero) x=(-7-**√29**≈-12.3) Answer is≈-6.1(second zero By Bobby 13oyce  Quadratic  Equation Song     Song by Ms. Suddath media type="file" key="Quadratic_Formula.wav"
 * 5.4÷2 _Division**

FINDING THE ZEROES:** 
 * [[image:0.jpg]]picture from google images

Finding Zeros ||

Step 1:enter the equation into the y= section and hit graph Step 2:Once into graph click second and trace to get to Calculate step 3:in Calculate press the number 2(zero) and it will take you back to the graph screen step 4:enter the left bound and the right bound then guess the zero. the calculator will find the zero between the 2 bounds. you have to do that to both sides of the line. an easy way to remember this is to just find the X intercept. in this case the zeros are -2.8284 and 2.828 [] page created by Joseph Snyder **  [|**summary of all methods**]
 * To find a zero on a calculator is very easy.we will use a simple equation:Y=X^2-8
 * SUMMARY:**