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⇒ s′(t)=4(2t−3)(8−2t)^3−6(2t−3)^2(8−2t)^2
how can i factor this? I keep factoring incorrectly :(
 8 months ago
 8 months ago
⇒ s′(t)=4(2t−3)(8−2t)^3−6(2t−3)^2(8−2t)^2 how can i factor this? I keep factoring incorrectly :(
 8 months ago
 8 months ago

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PaynesdadBest ResponseYou've already chosen the best response.0
Show me what you have done.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
How many (2t3) can you pull out?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
I used 2 to factor since it goes in both 4 and 6
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
ok so that is part of it
 8 months ago

PsymonBest ResponseYou've already chosen the best response.1
\[4(2t3)(82t)^{3}6(2t3)^{2}(82t)^{2}\] \[(2t3)(82t)^{2}[4(82t)6(2t3)]\] I'll stop here as to not go all the way, but maybe you can see what I was doing?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
The problem is im not sure how to factor these anymore. i did a similar problem like this.. only they factored out an outer number and here: we factor one of the insides number. im so confused.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Do you follow what @psymon did?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
yes but why can't we pull out a 2 in the outside since it' can go into 4 and 6?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
ok I have dealt with this before ... it is tough to see. There really are only 2 terms in your original equation...do you see that?
 8 months ago

PsymonBest ResponseYou've already chosen the best response.1
Because I rather not do too much at once and worry about mistakes.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
and no i didn't follow... this is where im stuck
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
But Psymon could have done that too.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Look you actually only have two terms with several factors each. Hang on..
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
The first term is 4(2t3)(82t)^3
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
That is one big term because it is composed of things being multiplied together (called factors)
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
the factors of the first term are 4, (2t3), and (82t)
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
So what would be the 2nd term? @mathcalculus
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
6, (2t3) and (82t)
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Good so now think of factoring something easy... like 6x^215x ... you factor out the common factors and leave whatever is left ... right?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
In other words you factor out 3 and x and leave (2x5) right?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
So now look at your equation ... what things and how many can you factor out of both terms
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
thats what i was saying... 2 goes in for 4 and 6..
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Ok what other factors can you factor out?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i can factor (2t3) and (82t)
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Right how many 2t3 can you factor out remember you can only factor out as many as the least number in either of the two terms.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
right and how many 82t?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
@Paynesdad right i know i can factor that too but what about the outer numbers. should i factor that firsT?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
you can it shouldn't matter.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
so factor out 2(2t3)(82t)^2 and show me what you are left with
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
yes it does.... for ex::
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
see they factored out using the 4
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
That doesn't dispute what I was saying it doesn't matter if you factor out the 2 right now or not.
 8 months ago

PsymonBest ResponseYou've already chosen the best response.1
dw:1375832092218:dw This is just how I might go about doing these on paper. Looks like you're getting closer to understanding though, @mathcalculus ^_^
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i want to know why can't i in this problem. which confuses so much.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
You can factor out the 2...You can do it now or you can do it in the end ... either way you will end up doing it. I, personally, would do it in the beginning.,,
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
@Psymon is choosing to do it at the end...it will get done ... it's just a matter of when
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
so factor out 2(2t3)(82t)^2 and show me what you have and I will tell you if you are right.
 8 months ago

PsymonBest ResponseYou've already chosen the best response.1
I'm personally too focused on the parenthesis terms and not making mistakes that I kinda just leave the coefficients til the end. Its dividing out those groups that worry me the most :P gtg now, though, good luck @mathcalculus
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
@Psymon got it^_^
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
that helped out alot. then what?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
don't i need to finish?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Show me what you have. so far.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
2(2t3)(82t)^2[2(82t)3(2t3)
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
now simplify what is in the b
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
what about the left side?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
no don't just the stuff in the brackets
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i got [164t6t+9]
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
errrrrr no rethink that last step
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
there's no where to go. now what about the left side.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
So now write it out again (yes the whole thing)
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
2(2t3)(82t)^2[10t+25]
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Good now is there anything else that can be factored out now that you combined that last factor (notice you didn't multiply out that factor before just INSIDE of the parantheses of that last factor
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
let's say im loooking for the critical points.... i would still need to follow to this step right?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
yes it is in deed helpful.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Nope there is something you can pull out of the last factor...
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
no Look > (10t+25)
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
oh i thought you meant only from looking at the left side.. :?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
There is no side it is just one big thing...
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
well what are you factoring out of the last factor?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
ok so do that and combine it with the 2 in the front and rewrite it one last time...promise.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
2*5(2t3)(82t)^2[25]
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
You factored out a 5 and had what left in the parantheses
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
you mean in the brackets t+25
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
No it was (10t+25) if you just had this and factored out 5 what would the result be
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
right welll you can't just throw that out...So now you should have all together...\[2(2t3)(82t)^2(5)(2t5)\] right?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Now normally we combine our any numerical factors so we would bring the 5 to the front and multiply it by 2 and get 10
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
So the final answer is \[10(2t3)(82t)^2(2t5)\]
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Looking at the final answer ... how many terms are there?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
nope remember terms are things that are separated by + or  and not in parantheses.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
For example 5x+2y +16x^2 is three terms
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Right only 1... Now how many factors in that 1 terms?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Factors are things that are multiplied together so 6xy has 3 factors.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
7(x+1) (x2) has 3 factors too
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
this is confusing me more.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
yep three things multiplied together... good
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
for a small problem.. it's so long..:?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Well actually 4...10, 2t3, 82t, and 2t5
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
...I know ... do you want to know why this form of the equation is better?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
ok it has to do with this rule...if xy=0 what do you know?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i have to keep going... it's getting too late for one problem:/
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
is it possible to show me so that i can how...
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
well If I am thinking of two numbers and I tell you that they multiply to 0 can you tell me what one of the numbers I am thinking of?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
right! so look at the original equation...if you set that to 0 you cant solve for t
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
omg obvious......
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
but if you get it into this form \[10(2t3)(82t)^2(2t5)=0\]
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
it's the factoring i need help with. that's all
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
whats next after that.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
ok I just wanted you to see how it helps you in actual calc problems but I understand...next? no next ...\[10(2t3)(82t)^2(2t5)\] is completely factored you did it.!
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
are you sure? look how simple this person did this problem ds(t) / dt = 4 (2t  3) (8  2t)^3  6 (2t  3)^2 (8  2t)^2 = 0 ==> factoring: (2t  3) (8  2t)^2 (4 (8  2t)  6 (2t 3)) = 0 ==> (2t 3) (8  2t)^2 (50  20t) = 0 so the three critical points are: t = 3/2, 4, 5/2.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
im looking for t right.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
they've multiplied 10 to 2t5
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
but why? the last one?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
not the 1st, nor the 2nd?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Right that is exactly what you had but YOU factored the 10 out...they didn't.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
Hang on you are thinking of distirbution
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
you don't distribute over multiplication !
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
this is taking forever.. for a small problem ___
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
thank you for you help @Paynesdad really appreciate it.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
5(79)(3)(2)...you can muliply the 5 times any one of those numbers but not all of them ...I would ppick the last one but we could multiply any of them just not all of them
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
No problem ... Good luck in tough subject but honestly
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.0
you have a better comprehension then 50% of the students I have had. @mathcalculus
 8 months ago
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