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Good day students welcome to mathgotserved.com in this clip were going to be going over how to factor polynomial equations rights it instructions are for us to factor completely question number one what if we have the polynomial equation X to the fourth plus 4X to the third plus 3X square +12 X equals zero now the goal is to factor this equation completely so first thing to do anytime you factoring is to inspect every single term and ask yourself is there a greatest common factor that I can extract from every single term in the original problem so let's take a look at the coefficients we have one for 312 there is a call factored here what if we look at the variables we have X to the fourth X to the third X to the second power and X of the first power now theall variables of the same all the same variable with varying degrees in that orientation configuration the smallest power is normally the GCF so we have 4321 there's a one here so the GCF is automatically going to be X to the first power because X of the first power evenly divides every single variable express out term here okay so what were going to do is factor out that's greatest common factor which is X now this is the deal whenever you are factoring out the greatest common factor what you doing is you dividing every single term by that with his common factor that has in factored out okay so what we're doing in essence you don't have the right is down is you dividing every single term by X we are gonna have a reduced form of this the left side of this equation because we just took out the greatest common factor now will carryout that step you going to be left with X to the what's power now remember anytime you're dividing exponents of the same term let's see have X to the and power divided by X to the and power through the property of exponents known as quotient property of exponents it says now whenever you dividing exponents of the same base you subtract the exponents okay that's what were going to do here if you take out X from the first X to the first power from X to the fourth power you just subtract one from for you end up with X to the third okay plus if you factor X from four exited third you end up with 4X square plus 3X +12 okay now let's take a look at the quantity in the parenthesis now what's we have in the parentheses is a cubic polynomial with four terms so how do we proceed to three have four terms of use of the quotes you factor by grouping okay so the viewer of the terms by two place our partitioned to the left of the middle sign and then will ask ourselves is there a greatest common factor for the two terms to the left of the partition and the answer is yes is bring down this X the greatest common factor between X to the third in 4X square look at the exponents the smallest two so we automatically know is going to be X to the second power now what we factor out X square from these two terms is as though we dividing both of them I X square will be left with X +4 okay now will direct your attention to the two terms to the rights of the partition and laughter so the same question is very greatest common factor that can be extracted from these two terms remember the answer is no you can always factor out one right this sign here always determines the sign of the term that's factored out so you is drop down the sign of our there and then from these two terms the GCF is clearly three so he factor out three and we left with X +4 because we dividing two terms by three that's what we end up with okay now one way to check to see if you are factory by grouping is correct is by examining the quantities in the parenthesis in the identical then that's a clue that's your doing you work correctly so that's the case here so we may proceed to bring down the X the two quantities in the parenthesis that are identical can be factored out to give you X +4 in the outside there is the GCF so we factor out from both sides of our partitioned will be grouped together in their Om with apprentices X square +3 equals zero now the question is can I factor any of these further this cannot be factored the monomial this is a linear binomial there is a GCF that can be factored out because we were to address that earlier on now let's take a look at this right here there is a formula called the difference of squares formula okay the friends of squares what is that formula will it's a square minus be square equals a pleasant be times a minus B so what is formula called this is that anytime you have a difference of two squares it can be factored further the procedure just involves taking the square root of the first and the second term and express in them as a Psalm and the difference okay the question now is is this formula the

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