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the best solution is to factor the "sums" so that you can see the parts that multiplied together to get them. then you can cancel out like "terms" top to bottom
do you know how to "factor" the sum parts?
No not really I just started this stuff I don't understand it much at all
I can try to teach you how to factor if you want.... or do you simply want the answer to the problem :)
Teach me step by step :)
ok..the basic rest in this simple fact... 3(8) = 24 its not the numbers here that are important, but the way we are going to work them that counts.... but Im starting simple. You agree that 3(8) = 24?
Yes I do agree
good, then this should be the same: 3(6+2) = 24 ... do we agree?
then the "rule" that allows us to know this is called the "distibutive property". We are going to "distibute" that (3) thru the (6+2) to get our answer like this: 3(6+2) = 24 3(6) + 3(2) = 24 18 + 6 = 24 24 = 24 ..... does that make sense?
distribute is the proper spelling :)
Yes that makes sense :) it's just I don't understand the problem I put down on here
i know...but we have to establish the "rules" for solving this problem since you say that you are unfamiliar with them.... ok? to solve your problem we need to do the "opposite" if distributing...I simply call it unDistributing.or factoring
Ok I see :)
2x-10 can be unDistributed.... we need to find a numbe that both 2x and 10 have in common so we can pull it out of our way...that number is called the "greatest common factor"...adn simply means the biggest number that they have in common when they are in factored form.. 1(2) are the factors of "2" 1(10) 2(5).......are all the factors of 10. now what is the biggest number that they have in common now that they are in factored form?
does "2" have 5 as a factor? I cant see it :) the biggest number that these have in common would be a "2", that is what they have in common right?
Oh I see now :)
then lets "unDistribute" that 2 and see what we get: 2(x+5) looks about right. we can double check ourselves by "distributing" it together again: 2(x+5) 2(x) + 2(5) 2x + 10 ...yep that works.... you see it?
good, then we can try our hands at that "quadratic" expression... quadratic is just some fancy latin name meaning "highest exponent is a '2'...
ok good :)
And I see a typo I made above..... 2(x-5) is what we wanted from that....... x^2+7x+12 is tricker but it has the same "basic" concept as before...there are 2 "numbers" that multiply together to get this expression. but they are in the form of: (1+2)(6+2) = 24 which is more complicated...
that +12 hanging out on the end...we need to know all the ways we can factor that out. 1(12) = 12 2(6) = 12 3(4) = 12 ....these are our possible options to work with, do you agree?
yes I do agree completely :)
yay!! you see that middle term? that (+7)? it wants 2 numbers that are added together to make it a +7. Lets try to see if we can use our "pool" of numbers to get us some answers: 1+12 = 13 ....not 7 2+6 = 8 ......still not 7 3 + 4 = 7 ...... we found a winner!!
now we need to set it up like this: (x+3)(x+4) double check ourselves: (x+3)(x+4) (x+3)(x) + (x+3)(4) xx + 3x + 4x +3(4) x^2 + 7x + 12 .... it fits...
like I said...more complicated, but still the same basic rules.... so we have this now: (x+3)(x+4) (2)(x-5) --------- ------ (x-5) (x+3) any like "terms" cancel each other from top to bottom. That means each (.....) that is the same on top and on bottom can be crossed out. (x+3)(x+4) (2)(x-5) --------- ------ (x-5) (x+3) what can we cross out?
(x+3) and (x+5)
thats right.... adjusting for typos that is ;) so lets get rid of those "values" and what we have left is: (x+4)(2) which is a perfectly good setup, but some tests may want you to write it out in its "distributed form: 2(x) + 2(4) 2x + 8 is another way of writing it
Ok I see I think I have the answer to the problem now is it 2(x+4)? that's what my worksheet said. I just had to show my work to get the write answer.
right I mean*
2(x+4) is a fine answer..... and is accepted at all the finer establishments thru town :)
Yay! I got it correct! :)
I need help again on this problem: x^2-3x-10/x+7 times 3x+12/6x-30