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Part2 factoring

Added Apr 28, 2020 •

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Sorry about missing the first minute of the video with the first example- my kids interrupted. This reviews quickly multiplying, factoring with leading coefficient 1 and factoring with a lead coefficient of another number.

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hey what you can also set up a box you can do that and say x + 1 and then x + 8 x x squared x 1 x 1/8 * 1 is 8 add up your light terms do you get x squared plus 9x Plus 8 same thing can I do one more month how's your free deposit video Try it yourself to make sure you still know how to do that 3D T-Rex kind acts there's our first term is 2x squared are outer term to act * 5 is going to be 10 X or interterm -1 * X is -1x and the -1 * 5 is -5 and then are outer and inner turn charity Starlight terms we can combine those 10 x -1 x is 9 X so 2x squared + 9 x - 5 and that's our final okay so now it's factoring trinomials for doing the opposite of what we just did do you want to factor X squared plus 8X plus 7 so we always first look for a greatest common factor I'm in the ocean is one there's no other factors other than one that we can take out first so then let's look at just setting up our two sets of parentheses were the first one x x x right there that becomes our first turn here x x x gives you a square okay then we look at that last term so 1 * 8 up here Davis at 8 just like overseer -1 * 5 + -5 so the last time we put up your house of x to give us at this is like our first term and Foyle this is our outer plus our inner terms added together has to equal a fax and then this is our last term 7 now the only multiples in order to get 7 or 1 * 7 so it put a one here and a seven here and we need to get a positive 7 which means that they either both have to be positive or both have to be a negative but since the middle term have to add up to give us a positive choose the positive Xbox One X x + 7 now in all of these in this is our final answer for our factoring now in all of these always multiply make sure you get back what you started x x x gives you x squared x * 7 is 7 x 1 x x is 1x + 1 * 7 is 7 7 x + 1 x kisses that a tax so once you check it okay that means we factored krait correct x + 1 x x + 7 let's look at another one k squared - 10K + 24 so greatest common factor their first term after multiply to give its case where it's okay and K now we need multiples of 24 so we could do One X 24 2 goes into it 2 x 12 3 goes into it 3 times 8 and then 4 goes into it four times six and 5 is not go into that sweetheart my two pairs to try and when we look at that middle term the middle teachers have to add up to give us a negative 10K Sota multiply to get a positive add we get a negative that means we went all of these pairs to be a negative times a negative to give us that positive since that middle term has to be a negative so let's put a negative signs in there and let's see which care will add up they give us a negative 10K so if you do negative one negative 24 that's -25 negative to negative 12 at -14 is -11 and the -4 and -6 given us -10 so that's what we want -4 and -6 not remember you might put two numbers there but then if you multiply and you get the wrong middle term and try another you might be the Cs and do just fine there but you may have to cross it off or erase it and try again and again always double-check it so we get K squared MK * -6 is -6 -4 k 86 * -4 is -24 and the -6 + -4 give us- tents that checks out for final Factor K - 4 * K - 6 now if you would have written K - 6 first and then the kmise for same thing still correct hey let's do a couple more like this and I will get you some a little harder so J squared - 13 J + 42 so let's let's set up our Francis he's our first term comes from j-squared so J&J and then let's look at multiples this comes from our last term so multiples of 42 while we could do 42 + 1 we could do to Chico 2 * 20 really should go into it the trick with the three is if you add four plus two sticks and 3 goes into 673 goes into 4 I can't think of off the top of my head but that is so you can always divide 3 goes into 4 Once he goes into 12/4 and 14 * 3 * 14 as a factor not go into 42 * 4 * 10 is 40 6 * 7 is 42 and that's our closest pair I wasn't going to it xbx1 okay signs next to multiply to get a positive 42 which means they're all positive or all negative but since the middle term is negative they have to add you get a negative we're going to choose negative for both of them and we want to know okay what's good to add up to give us a negative 13 if they're both negative -6 + -7 + 14/8 + 3 we want to look at which pair in the pair that could add up to give us -13 is a -6 + a -7 l - 6 - 7 again we put up with the Minor 7 first doesn't matter always X and make sure you get back what you started with is -6 negative 7 gets you -13 years are actor hey let's look at one more of these x squared plus 3x minus 40 okay then we need x and x for a first one and what multiplies to give us a negative 40 okay so since we're multiplying to get a negative that means one has to be a positive one has to be a negative that might get a little tricky but let's look at factors of 41st 40 + 1 20 + 2 4 + 10 5 + 8 fixing to go in at 6 X 7 42 obviously okay 7. Going to work either so here's our Factor one has to be positive one has to be a negative and when we add them up we have to add to get a positive 3 over adding a 7 in the negative and our answer is going to be a positive then that means that the bigger number has to be a positive number so I know of are pears let's make the bigger number positive in which pair is going to add up to give you a 3 + 8 + -510 + + -4 but you might have already kind of saw that ain't positive 8 and -5 add up to give you a positive 3 no + 8 + a - 5 it's also worth noting sometimes these are not factorable UK every single parent you can't find one that works sometimes you just can't Factor it so here's our answer x + 8 x - 5 okay let's get to some harder one has the first coefficient is not a one so the rule of thumb is always look for a greatest common factor first so let's look at the numbers 303 and a  with those in the all of those at 3 Izzard DCF what we're doing is distributive property backwards you can't take out an axe cuz the last time does not have an X to take out at 3 the three times what gives us x squared so that's going to be x squared + 3 times what gives us three acts so act -3 times what gives you 6 and that the -2 and we've got a trinomial now that we can try to factor further sometimes it doesn't work sometimes we're done here we can certainly try XNX golden the first thought our last term is a -2 which means that to multiply to get a negative to you could either do 1 * -2 can do a negative one time two positive to get two choices there and we need to add to get a positive one so which pair is going to give us a positive one so we need number to be positive so I didn't choose the positive to the negative 1 so x + 2 * X - 1 here's our final answer I think another harder one six x squared minus 5x plus one okay go this one it does not have a greatest common factor there's nothing that goes into both 65 and one other than one itself okay so now this gets tricky because we've got different options for that first turn go to make us 6 x squared we can either choose a 6S and a 1x or we can choose a 2X and a 3X so I like to when we've got different options for that first term I like to write him vote cuz then we can kind of play around with the different numbers now this one's not as bad because to multiply to get 1 weed eater got positive One X positive 1 or negative 1 times negative 1 why would you choose negative 1 times negative 1 but if you look at that middle term is a minus time outer and inner term have to add up to give us a negative 5 so that's why we're going to choose the two negative signs we know that has to be the case so in all of our different possibilities to the negative and then we can choose the one in the one and sometimes if these are different numbers you can you know mix him around cuz it does matter the place value and what they're multiplying two so it looks like we're going to have to check each one at 6 and that's a six x squared -6x -1x + 81 * -1 is + 1 -6 x -1x that gives is -7x that's not going to work there's no other numbers to switch it around so you just ask that off this one works x * 3 x + 6 x squared 2x * -1 is -2X -1 * 3x is -3x and 1 * -1 is + 1 negative 2x - 3x + are there in -5x and that's what we want that means that our final factoring 2x - 1 x 3X - 1 Vanessa britting okay let's try to just two more OKC next one for x squared plus 4x - 3 Sotto sopra first term there is no GCF performing at 3 I'm so this is another one that's going to have two possibilities for that first term we could do a 4X and a 1X to act 2X I'll give you a 4 x wired different possibilities okay so now I multiply to get -3. Two possibilities positive 1 * 9 3 or we have a negative 1 times positive 3 so this one in the place does matter and all of these so we might have some scratch marks moving around sometimes it's good that you know sometimes you know just start plug-in stuff in and see what works we could do you a one and a -3 there and sometimes it's good just to start multiplying to see if that works so if you check your I'm going to just skip to the inner and outer terms to suppose we need to get a for ax in the middle we got a 1x there -12x know when you see that big of a difference and we need to get a 4X in the middle that's going to give us -11 X we don't want to have to multiply the three in the four together so let's move it around I'm going to put the positive 3 here -1 here so far x + 3 * X - 1 so let's try this again middle term 3x and then outer turn -4x positive 3 negative for is -1 even if we switch the sign we're not going to get a positive for so we can just kind of throw this away for now we can make something work down here we need to get A+ for so let's not let's choose the positive 3 in the negative one and see if we can get that to work so interterm 2x * 3x is 6x and outer terms 2x - 1 is -2 x 6 x - 2x there's are 4X if we would have gotten a negative 4X we could have just switch the signs around so here's our final answer to x + 3 x 2 x - 1 I like the kind of rewrite this and then just double-check that mold playing one more time directions to X's 4x squared 2x * -1 is -2X 3 x 2 x 6 x 3 x 2 - 1 is -3 and they're there it is the 2x + 3 * 2x - 1 is our final answer okay last one 18x squared - 15x - 18 I remember a couple times ago we went always check for a greatest common factor 18 and 15 to have a greatest common factor so 3 goes into all of those so let's make the smaller and take the three times what will give us 18 x 6 x 3 will give you 18 and then add in the x squared -3 * 5 will give you what the heck * -3 * 6 I'll give you 18 you can multiply that back to make sure you get what you started with all right now we've got that quadratic trinomial no GCF there we took out the biggest one and now we're going to keep that 3 there but we need to think about what multiplies to give us 6 x squared so you could do six in one or you could do three x and 2x so again just like we did over here with the two different thing you want to send them both up still has the three on the outside and we could do a 6X in a 1x or just text or we could do a 3 with a reacts and it's too wet so we need to multiply to get a negative 6 and then add to get a negative 5 but two things different things are going to be multiplied so let's just work on this for right now so we could do 2 * -3 to the negative 6 you could do a negative 2 times positive 3 EDD deposit is 6 * -1 or a negative 6 times positive one to get a negative test now it's just a matter of finding the right places and the right signs of what you're going to pick this there is a lot to work with here now and we just focus on this not the outside three are middle term needs to be a negative so the more you do this the more you kind of see like we would if we wouldn't want to play if we chose the six in the one here you wouldn't want to choose a six over here because then sick time this text 36 is going to be too big to add to get a negative 5 a little things like that and we could put a 6 year and a one here and so okay I -1 they may be apart next year it's our middle term would be 6X + a -6 XS could add a zero we don't want that so maybe in this scenario we're going to look at the two and three and maybe a positive 2 -3 kind of messy specially if you're using pattern you get a positive 2x + a -18 / that's way too big even if we put the two there two times 6 is twelve that's still 82 Bagless the name is as good once you see that you're not getting anywhere with one parent lets done and the other pair so we can you know try to 6 in the water the two and three maybe try the two in the three okay well you've got interterm is Borax powder term is 9 acts remember one of these has got to be positive one has to be negative we need that difference to be a -5 the Fitzroy negative and fish were a positive that would add up to be a negative 5 so we need these threes so we are going to put a minus sign right 3 * 3 is -9 an appositive here 2 * 2x is 4X -5x again multiply it and I know it takes a lot of work to multiply we can skip that three part and then just make sure that these to multiply to give us 6 x squared minus 5x minus 6 for 3x x 3 x 6 x sqrt 3 x X - 3 is minus x 2 x 2 is 4X 20 * -3 is now you're sick so we get 6 x squared minus 5x minus 6 there's rfactor

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Part2 factoring

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