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mathcalculus
 2 years 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 :(
mathcalculus
 2 years 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 :(

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Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Show me what you have done.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0How many (2t3) can you pull out?

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

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0ok so that is part of it

Psymon
 2 years ago
Best 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?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1The 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.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Do you follow what @psymon did?

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

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0ok 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?

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1Because I rather not do too much at once and worry about mistakes.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1and no i didn't follow... this is where im stuck

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0But Psymon could have done that too.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Look you actually only have two terms with several factors each. Hang on..

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

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

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

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0So what would be the 2nd term? @mathcalculus

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.16, (2t3) and (82t)

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

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

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1thats what i was saying... 2 goes in for 4 and 6..

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Ok what other factors can you factor out?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1i can factor (2t3) and (82t)

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Right 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.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0right and how many 82t?

mathcalculus
 2 years ago
Best 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?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0you can it shouldn't matter.

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1yes it does.... for ex::

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1see they factored out using the 4

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

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1i want to know why can't i in this problem. which confuses so much.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0You 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.,,

Paynesdad
 2 years ago
Best 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

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

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1I'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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1that helped out alot. then what?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1don't i need to finish?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Show me what you have. so far.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.12(2t3)(82t)^2[2(82t)3(2t3)

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0now simplify what is in the b

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1what about the left side?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0no don't just the stuff in the brackets

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1i got [164t6t+9]

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0errrrrr no rethink that last step

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1there's no where to go. now what about the left side.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0So now write it out again (yes the whole thing)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.12(2t3)(82t)^2[10t+25]

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Good 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

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

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0yes it is in deed helpful.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Nope there is something you can pull out of the last factor...

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0no Look > (10t+25)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1oh i thought you meant only from looking at the left side.. :?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0There is no side it is just one big thing...

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0well what are you factoring out of the last factor?

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.12*5(2t3)(82t)^2[25]

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0You factored out a 5 and had what left in the parantheses

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1you mean in the brackets t+25

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

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

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

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

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Looking at the final answer ... how many terms are there?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0nope remember terms are things that are separated by + or  and not in parantheses.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0For example 5x+2y +16x^2 is three terms

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Right only 1... Now how many factors in that 1 terms?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Factors are things that are multiplied together so 6xy has 3 factors.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.07(x+1) (x2) has 3 factors too

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1this is confusing me more.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0yep three things multiplied together... good

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1for a small problem.. it's so long..:?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Well actually 4...10, 2t3, 82t, and 2t5

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0...I know ... do you want to know why this form of the equation is better?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0ok it has to do with this rule...if xy=0 what do you know?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1i have to keep going... it's getting too late for one problem:/

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1is it possible to show me so that i can how...

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0well 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?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0right! so look at the original equation...if you set that to 0 you cant solve for t

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1it's the factoring i need help with. that's all

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1whats next after that.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0ok 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.!

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1are 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.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1im looking for t right.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1they've multiplied 10 to 2t5

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1but why? the last one?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1not the 1st, nor the 2nd?

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Right that is exactly what you had but YOU factored the 10 out...they didn't.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0Hang on you are thinking of distirbution

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0you don't distribute over multiplication !

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1this is taking forever.. for a small problem ___

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.1thank you for you help @Paynesdad really appreciate it.

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.05(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

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0No problem ... Good luck in tough subject but honestly

Paynesdad
 2 years ago
Best ResponseYou've already chosen the best response.0you have a better comprehension then 50% of the students I have had. @mathcalculus
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