This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
Make sure the word gets out to Mr. Ryan and Mr. Paul that they missed an intriguing class today and that they should check the website for printable problem sets AND that they should check with their (ahem) friends for missed notes and concepts...
Mr. Ryan and Mr. Paul... please contact me via email or this blog so that I know you are awake!
The FACTORED EXPRESSION is 5x(x+9). The SIMPLIFIED EXPRESSION is 5x^2+9x.
That's it.
Just like when we are combining like terms with:
5(x+7)+3x... is that it? NO 5x+35+3x... is that it? NO 8x+35... is that it? YES, we can't combine anymore!
When you are factoring, you look for a) common factors (such as 5x above) b) special situations (in our case, like quadratic trinomials... there are no common factors, but we know that quadratic trinomials are sometimes "factorable" with the help of the area model and diamond problems!!
I would suggest that you phone a friend and make yourself a little miserable in the meantime... if anyone would like to join Paul tomorrow, just let me know.
I'm stuck on #2 & #5. For #2, I put b^2 in the bottom left corner of the area model, & I put -20 in the bottom right. Is it supposed to equal 1 when I add the other boxes together?
Pls be more specific with problem #'s... i.e. from the problem set or a page in the text book.
If you are talking about #4 on page 508, yup, it's a toughie, but doable.
Factor: 6x^2-11x-72
6x^2 in the lower left and -72 in the upper right.
That means you are looking for two numbers that sum to -11 and have a product of -432. A little bit of trial and error with factors of 432 will get you to 16 and -27, yes.
Now, you'll have to play with the area model a little... your math intuition should tell you that 3x and 2x will work better than 6x and x as "anchors" for your binomials.
Let me know how you do.
I hate to say it this way, but 15,17,&19 are pretty straightforward examples of using the area model. #4 was the toughest problem in the list.
Your comments on #2 above scare me. Why would you put b^ in the lower left and the constant (-20) in the lower right. The squared term and the constant term MUST be diagonal from each other in a binomial area model. That was the whole point of us observing all of the patterns when we did the multiplication, yes?
I don't know what you mean by the question "is it supposed to equal 1"... the cross-products of the coefficients in a 4-region area model will be equal... ?????
Never trust a math teacher!! But you ARE having FUN right? You know that feeling when you just hope that a problem set will never end!!!??? That happens to me sometimes, too!!
OH MY GOSH!!!!!!! I JUST REALIZED WHAT I'VE BEEN DOING WRONG THIS WHOLE TIME..... I HAVEN'T MULTIPLIED THE TOP RIGHT CORNER COEFFICIENT BY THE BOTTOM LEFT CORNER COEFFICIENT...
NOOOOOO!!!!!!!!!!!!!!!!!
Mr.C, do I have to go back & redo all of the problems I've done in the packet? =(
I think I'll come in for lunch to, I can do the problems but they take me long time and there is probably some easier way to solve the diamonds aside from random guessing and checking.
For problems like #17 in the book, do you have to multiply -36 by 2 & then try to figure out the factors? Or is there a simpler way than figuring factors of large numbers?
for # 15-23 in book, it seems like there is some sort of thing I am missing of how to factor out square numbers, because unless there is a special trick or tool, it just seems insane.
(sorry for being late) I'd definitely like to join people for lunch. I think i have the basic concepts down but I must be missing something about the diamond problems. For several I tried all factors but couldn't find any that added up. (13, 14, 16, 17, 18, and 22)
I am realy confused on where to start for number 4, and i have no idea what to do for numbers 15-19. :(
ReplyDeleteWhere? In Problem Set 8A?
ReplyDeleteMake sure the word gets out to Mr. Ryan and Mr. Paul that they missed an intriguing class today and that they should check the website for printable problem sets AND that they should check with their (ahem) friends for missed notes and concepts...
ReplyDeleteMr. Ryan and Mr. Paul... please contact me via email or this blog so that I know you are awake!
Dear Clueless,
ReplyDeleteI'll assume you are talking about the problem set.
#4 is a diamond problem (set up your area model and see).
#15 is also a diamond problem... the invisible "middle term" is 0n i.e.
n^2 - 0n - 16
Are there 2 numbers that have a product of -16 and sum to zero (hint: what must be true of any 2 numbers that sum to zero??)
#16 - Factor out a common factor first and you gotsk yourself an easy-schmeasy diamond problem
#17 - ditto with #4
#18 & 19 - ditto with #16
Remember, if you remember the area model symmetry and equalities and your diamond problems, FACTORING IS FUN & EASY!!
Mr Chamberlain....
ReplyDeletemy mind went blank in the first few problems of the set 8a....
when factoring a problem with no middle, like #1 - 5x^2 + 45x which I simplified to 5(x^2 + 9x) - how do you completely factor iit?
You almost got it... you could have also factored out an x, yes? But that's it!
ReplyDeletelike im done factoring it?
ReplyDeleteSo what did I miss today in class? Anything I need to stay for lunch or after school for?
ReplyDeleteYup!
ReplyDeleteThe FACTORED EXPRESSION is 5x(x+9).
The SIMPLIFIED EXPRESSION is 5x^2+9x.
That's it.
Just like when we are combining like terms with:
5(x+7)+3x... is that it? NO
5x+35+3x... is that it? NO
8x+35... is that it? YES, we can't combine anymore!
When you are factoring, you look for
a) common factors (such as 5x above)
b) special situations (in our case, like quadratic trinomials... there are no common factors, but we know that quadratic trinomials are sometimes "factorable" with the help of the area model and diamond problems!!
Like I said... FUN & EASY!!
Paul - You need to visit mathchamber unit 8 and print out the hw problem sets. There is hw in the text book, too.
ReplyDeleteYou need to chat with a friend or two and get some coaching on factoring using the area model.
It probably wouldn't hurt to schedule some extra time with me, either during lunch or after school tomorrow.
Ok, I can come during lunch tomorrow!
ReplyDeleteI would suggest that you phone a friend and make yourself a little miserable in the meantime... if anyone would like to join Paul tomorrow, just let me know.
ReplyDeleteSorry Mr. C you are wrong, I'm not sure weather to put on a smilely face or not but it is actually in the workbook
ReplyDeleteI'm stuck on #2 & #5. For #2, I put b^2 in the bottom left corner of the area model, & I put -20 in the bottom right. Is it supposed to equal 1 when I add the other boxes together?
ReplyDeleteOoooh I got it, are the top left & bottom right boxes for #2 -4b & 5b? Sorry I just didn't think! =)
ReplyDeletePls be more specific with problem #'s... i.e. from the problem set or a page in the text book.
ReplyDeleteIf you are talking about #4 on page 508, yup, it's a toughie, but doable.
Factor: 6x^2-11x-72
6x^2 in the lower left and -72 in the upper right.
That means you are looking for two numbers that sum to -11 and have a product of -432. A little bit of trial and error with factors of 432 will get you to 16 and -27, yes.
Now, you'll have to play with the area model a little... your math intuition should tell you that 3x and 2x will work better than 6x and x as "anchors" for your binomials.
Let me know how you do.
I hate to say it this way, but 15,17,&19 are pretty straightforward examples of using the area model. #4 was the toughest problem in the list.
Your comments on #2 above scare me. Why would you put b^ in the lower left and the constant (-20) in the lower right. The squared term and the constant term MUST be diagonal from each other in a binomial area model. That was the whole point of us observing all of the patterns when we did the multiplication, yes?
ReplyDeleteI don't know what you mean by the question "is it supposed to equal 1"... the cross-products of the coefficients in a 4-region area model will be equal... ?????
Trouble on #15.. It seems like a simple problem, I just don't know what to do! There is no middle term, can I still do an area model?
ReplyDeleteI don't have the problem in front of me... but take a problem like x^2-9... no middle term, right?
ReplyDeleteWell, you could insert a placeholder middle term, like 0x (as in "zero" x), so then you would have...
x^2-0n-9
can you find two number that sum to ZERO and have a product of -9??? I think you can!!!
Okey dokey! Thank you!
ReplyDeleteThis packet is taking me longer than you promised.. =(
ReplyDeleteFor #23, I'm having trouble finding a pair of numbers that multiply to six but add to 0!
ReplyDeleteThere are a few prime polynomials in the packet!
ReplyDeleteNever trust a math teacher!! But you ARE having FUN right? You know that feeling when you just hope that a problem set will never end!!!??? That happens to me sometimes, too!!
OOOOOOH.. So a PRIME POLYNOMIAL, eh? =)
ReplyDeleteOf course I'm having fun!...
;)
I think there are 3 prime polynomials in the problem set 8A... can you find them?
ReplyDeleteI will be out for a while (another math party) some I'm hoping some of you can help each other!!
ReplyDelete3?!
ReplyDeleteI'm on the last 2! They better be prime polynomials, 'cause I've only found one!!
Can anyone tell me which the prime polynomial problems are? 'Cause I probably did something wrong if I only found one!
ReplyDeleteYes I agree with Mr.Chamberlain.. I'm hoping someone can help MEEEEEE!!
ReplyDeleteAhhh!!! I'm even stuck on #1 on pg 508.. I can't find 2 numbers that multiply to 16 & add to 5... =(
ReplyDeleteUgh same for #2.. And 2 is a prime number! The additives of 9 don't multiply to 2.. At all.. The book has answers for these but I don't understand!
ReplyDeleteHow can this be SO HARD?! I'm stumped on #4, too. I can't find any numbers that add to -11 and multiply to 72.. =(
ReplyDeleteCould I maybe stay for lunch tomorrow, Mr.C? With Paul & Ryan? I think I may need a review..
ReplyDelete-Lotta
For #5, for the answer in the back of the book, it says you cannot factor this equation because "there are no factors of 20 with a sum of 7".
ReplyDeleteThe equation for #5 is 2x^2+7x+10..
Where do they even get the 20 from?
I tried putting this equation into an area model, the only problem I'm having is I can't get the fraction relationships right..
OH MY GOSH!!!!!!!
ReplyDeleteI JUST REALIZED WHAT I'VE BEEN DOING WRONG THIS WHOLE TIME.....
I HAVEN'T MULTIPLIED THE TOP RIGHT CORNER COEFFICIENT BY THE BOTTOM LEFT CORNER COEFFICIENT...
NOOOOOO!!!!!!!!!!!!!!!!!
Mr.C, do I have to go back & redo all of the problems I've done in the packet? =(
I think I REALLY need to come in for review..
ReplyDeleteI did the whole packet with using that method... =((
ReplyDeleteI need help with #4 in the book.. How do I find factors of -432 that add to be -11?!
ReplyDelete..Yes, I'm redoing them..
I think I'll come in for lunch to, I can do the problems but they take me long time and there is probably some easier way to solve the diamonds aside from random guessing and checking.
ReplyDelete- Aaron
I can't get an answer for #15 on pg 509.. I can't find factors of -24 that add to be -13.
ReplyDeleteFor problems like #17 in the book, do you have to multiply -36 by 2 & then try to figure out the factors? Or is there a simpler way than figuring factors of large numbers?
ReplyDeleteAnd same for #19 as up there. ^^^
ReplyDeleteNobody wants to answer my questions... HELP!! =(
ReplyDeleteFor book #5, I can tell the problem just doesn't work, is there some principal that makes it impossible to do?
ReplyDeleteWould anybody like to come on algebra class chat with me?
ReplyDeletefor # 15-23 in book, it seems like there is some sort of thing I am missing of how to factor out square numbers, because unless there is a special trick or tool, it just seems insane.
ReplyDelete(sorry for being late) I'd definitely like to join people for lunch. I think i have the basic concepts down but I must be missing something about the diamond problems. For several I tried all factors but couldn't find any that added up. (13, 14, 16, 17, 18, and 22)
ReplyDeleteSame with me as for Paul!
ReplyDeleteAnd for #15-23, same for me, too!
I scrolled up & read about #4, & I got it!
ReplyDeleteI think you guys need some sleep... at least I'll have your attention in class tomorrow... I think!
ReplyDeleteIf you have been working on the homework for 60-90 minutes... THAT'S ENOUGH... you need to let your brain drain... I'm serious...
See you at 11:00 for some FUN!!
I NEED ULTIMATE HELP TOMORROW!!
ReplyDeleteOkay.. Thanks Mr.C.. See you tomorrow!!
ReplyDeleteI thought you guys were GOOD at the diamond problems???!!!
ReplyDelete