Good day students welcome to mathgotserved.com in this clip where going to be going over how to factor quadratic expressions or right the instructions for the examples that were going to be factoring are as follows we are to factor each expression completely okay right let's take a look at question number one let's say we have the quadratic expression X square +16 X +60 the task here is to factor this expression completely now when you have a quadratic to be factored the first anyone to ask yourself is what type of quadratic is this this quadratic is it trying no real the quadratic trend oatmeal so it if you have a scenario like this you want to think about using a method called the X game okay so the X games us follows we going to create on my foot of X where going to put AC on the top spot right here in beagles on the bottom now since we have this quadratic expression we written in descending order of degrees we can easily determine that a is equal to one the court fission of X square be is equal to 16 and see is equal to 60 so ACs one-time 60 that gives us extend the top and Ghia 16 that goes right on the bottom now it would take a look at this quadratic expression one tonight then indicated earlier was that if you take a look at a BNC you can clearly see that there is a common factor that we can extract okay so can go right into the factorization process now to play the game where going to ask ourselves the question what's two numbers multiply to give you 60 and out to give you 16 so some of you might easily determine what combination that is but sometimes you might have a problem where it is not obvious the combination the factor is that can generate the desired sum or difference in that case what you do is write down the target product in this case it is 16 and will just list all the parabolic is that multiply to yield 60 okay so let's start from the very first one 1×60 yield 60 now a combination of one and 60 yield 61 or 59 the target is 16 to this peer does not work will not the still going to 60 absolutely to goes into 6030 times this combination yields 32 or 2820 outer subtract that is a work is want to 33 goes into 6020 times now this combination yields 23 or 17 that's not the desired combination that we want so give ongoing okay will keep on going until we hit the desired of care that gives a 16 so will does for go into 60 that certainly does Vogels into 6015 times they combined this to some is 19 and the differences of 11 so that doesn't work either so move on to the next combination which is five this five going to to 60 if it does five goes into 60 of 12×5 get 1250+1060 yes so five goes into 6012 times this combination yields 17 or seven when he subtract that's not what we once we 116 Six goes into 6010 times right so if you add this to get 16 follow that's exactly what we want so let's group from this is the desired pair there's no need to continue on so we have six and 10 now ask ourselves to these numbers work anytime you populate your X game with numbers you must always test them to ensure that the work both the number and the sign okay so 6×10 a 60 good 6+10 is 16 excellent now in this case we have a situation where a is equal to one okay anytime you have a equal to one you do not have to Factoria by grouping you can jump directly to the factored state so we are going to factor this is X +6 since we have a positive six here times X plus $.10 a have a positive 10 there and that ladies and gentlemen is a factor form of the quadratic trend Romeo X square +16 X +60 okay let's take a look at question number two let's say we have X square -25 now look remember you want to examine whatever expression your given and ask is so what type of expression my deal with here if you take a look at this expression you notice that X square it is a square 25 is the square and you have in minus in between them there's a special terminology for expressions of this nature the called difference of squares aright and is a unique formula that can be used to really facilitate the factorization of the friends of squares if you have that formula mastered you can easily factor especially like this rather quickly okay so the formula the as follows if you have a square let's write this formula you have a square minus be square remember you need to have two squares on the minus this simply becomes the square root of the first plus or minus squared of the second the you going to write it as the product the product out the sum and difference of thesquare root of these two terms okay so we have a plus be times a minus the so this is the factored state of difference of squares so now we're going to apply this formula in the factor isolation of this difference of squares okay so to do that we're going to rip the first and the last term remember to both squares to taking you square roots should not be a problem and then we're going to write the sum and the difference of these two and express them of the product of

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