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Different Kinds of Factoring

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by

Pierre Lac

on 6 September 2012

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Transcript of Different Kinds of Factoring

By: Brittany Lac Factoring!!! GCF (Greatest Common Factor) Factoring You would be learning how to find GCFs in polynomials and monomials and binomials. A common factor is what the expression has in common with each set of numbers. GCF stands for Greatest Common Factor The number outside of the prenthesis is multiplying the inside. You multiply the number outside to each number inside. After finding the GCF you can factor it, meaning splitting the problem up. 2-Term Polynomial - DOTS In this you would be learning how to use the method of DOTS to factor 2-term polynomials. A square is made up of two exact numbers of itself and multiplied together to get a square. DOTS stands for Difference of two squares You factor the problem like in the first lesson If the first term (part) of the problem is a perfect square and the same with the last term, but needs to be subtracting and can only be two terms. Lastly you check your work using FOIL When you factor one term it has to be positive and the other has to be a negative. Since the negative and positive 10's cancel each other out, you are just left with the last two terms. FOIL stands for First, Outside, Inside, and Last There are two types of 3-term polynomials, this is one of them. You would be learning how to factor out simple 3-term polynomials. 3-Term Polynomial: Simple A simple polynomial is when the first term is squared with no coefficient. Polynomials is when there are more than 4 terms present A coefficient is the number that is before the variable (letter) in an expression. If you can't find any GCFs then you know that there isn't anything common yet. Since you know that the first term had a squared variable you can set up this formula or template. To factor a 3-term polynomial you first have to find the GCF. (x- ) (x- ) In the last term you need to find two numbers that can be multiplied and add together to get the middle term at the same time By placing that template you know the first term is squared and you can change the sign if needed. After finding the numbers you place them in the template. The signs would be positive in the this case, so they would be plus signs. There may be cases where there would be the need for one to be positive and the other negative. A 3-term polynomial: complex is a little like the simple one except for the fact that there are coefficient before the variable and you are going to have to factor it a little differently. 3-Term Polynomial: Complex There is this method called split the middle. The point is that you multiply the first and last terms together and see what can be added to get the middle term, but have the product of the two numbers. Complex polynomials are like simple exept for the part that there is a number as the coefficient. After putting the numbers in you group them together with two terms in each parenthesis.... After finding the numbers you would have to put the two numbers in the problem. Since out of both there is something in common with each other you'll only need one of them. Find common factors in each parenthesis like usual The other numbers would be placed together in there own parenthesis. Grouping 4-term polynomial is a little easy. All you have to do is put two terms in the parenthesis. Sounds easy right? 4-Term Polynomial: Grouping Since 4 terms are a little too big there is the need to group them together like you did before to work with them easier. 4-Term Polynomials are exactly what the name means. There are 4 sets If you don't see any GCFs? Then continue on. Before you do any of this you should find the GCF Everything would be like usual like you did in the previous lessons. You would factor like normally I don't think I should be telling you to do this all the time. USE FOIL TO CHECK ANSWER!!! Factor the whole polynomial If there was a GCF between the terms then you would do this.... Usually it's easier to group them with terms that are easier to work with Next you leave the number outside the grouping and group the inside and factor like normally Use FOIL to check your answer After factoring like normally you add the other term from the beginning back to the polynomial You're probably wondering what this word means and what it has to do with this slide. I can't tell you yet, but you would figure out later on Prime If there is nothing in comon with each other then you write down prime Prime means if there are no GCFs or anything in common wither each other. 15w + 21 3 5 7 3 GCF: 3 15w + 21 3 3(5w + 7) 5 x 5= 25 9 x 9= 81 3 x 3= 9 4x - 25 2 Check Check Check 4x - 25 2 2 (2x - 5) (2x + 5) negative positive 2 F: 2x * 2x= 4x O: 2x * 5= 10x I: -5 * 2x= -10x L: -5 * 5= -25 4x - 25 2 x + 8x + 12 2 12 6 + 2= 8 x + 8x + 12 2 USE FOIL TO CHECK ANSWER! O: x * 2= 2x
I: 6 * x= 6x
L: 6 * 2= 12 (x - 6) (x - 2) (x + 6) (x + 2) (x + 6) (x + 2) 2 F: x * x= x x + 8x + 12 2 4x - 15x + 14 2 coefficient 14 x 4= 56 -8 - 7= -15 4x - 8x - 7x + 14 2 (4x - 8x) (-7x + 14) + 2 4x(x - 2) -7(x - 2) (x - 2) (4x - 7) Use FOIL to check your answer O: x * -7= -7x
I: -2 * 4x= -8x
L: -2 * -7= 14 (x - 2) (4x - 7) F: x * 4x= 4x 2 4n + 8n - 5n - 10 3 2 (4n + 8n) + (-5n - 10) 4n(n + 2) + -5(n + 2) (n + 2) (4n - 5) 3 2 2 2 12p + 10p - 36p - 30p 4 3 2 2p(6p + 5p - 18p - 15) 3 2 2p (6p - 18p) + (5p - 15) 2p 6p(p - 3) + 5(p - 3) 3 2 2 2 2p(p - 3) (6p + 5) 2 x + 5 x + x + 1 x + 5x + 12 4xy + 3y - x 2 2 2
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