anonymous
  • anonymous
Factor 4sˆ5+16s³-32s-20 4s^5 is suppose to be 4s exponent5 but i dont know how to do it
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
What have you done so far?
anonymous
  • anonymous
nothing
anonymous
  • anonymous
Well, do you know how to find the factors of each term?

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More answers

anonymous
  • anonymous
cf is 4
anonymous
  • anonymous
That is a start. Pull a factor of 4 from each term and see what you have left.
anonymous
  • anonymous
4, 8, 5
anonymous
  • anonymous
No, I mean write the new expression after you factor out a 4
anonymous
  • anonymous
4(4s^3-8s-5)
anonymous
  • anonymous
Not quite. You're missing a s^5, but otherwise that's good.
anonymous
  • anonymous
Now what other factors do some of your terms have in common?
anonymous
  • anonymous
s
anonymous
  • anonymous
Ok, so factor those out from the terms that have it
anonymous
  • anonymous
not sure how
anonymous
  • anonymous
show me step by step plz and then explain
anonymous
  • anonymous
How did you factor out the 4?
anonymous
  • anonymous
4(4s^3-8s-5)
anonymous
  • anonymous
Right, but I mean what did you do?
anonymous
  • anonymous
Also that's not right
anonymous
  • anonymous
divide each term by 4
anonymous
  • anonymous
You keep forgetting the 4s^5
anonymous
  • anonymous
then what would it be
anonymous
  • anonymous
4(s^5 +4s^3 - 8s - 5)
anonymous
  • anonymous
But as I said, you can factor an s from the first 3 terms inside the parens.
anonymous
  • anonymous
Or rather, like you said.
anonymous
  • anonymous
And you would do it the same way. Put an s out front, and divide each term by the s you took away.
anonymous
  • anonymous
Just don't take one away from the term that doesn't have an s to start with.
anonymous
  • anonymous
s(^5+4^3-8-5)
anonymous
  • anonymous
No. What is \[\frac{s^5}{s}\]
anonymous
  • anonymous
idk im really bad with fractions
anonymous
  • anonymous
Then you should practice! =) Everything depends on everything else. If you practice your fractions until you are not bad with them, factoring will be a very fast process.
anonymous
  • anonymous
Lets start now. What is \[\frac{32}{2}\]
anonymous
  • anonymous
16
anonymous
  • anonymous
Ok, and if I said \[\frac{2^5}{2}\] ?
anonymous
  • anonymous
rawr!
anonymous
  • anonymous
a^5
anonymous
  • anonymous
What is \(2^5\)
anonymous
  • anonymous
32
anonymous
  • anonymous
Interesting. And what was \[\frac{32}{2} \] again?
anonymous
  • anonymous
16/1
anonymous
  • anonymous
Right.. Just curious, but what is 2^4?
anonymous
  • anonymous
rawr! rawr!
anonymous
  • anonymous
16
anonymous
  • anonymous
That's interesting. \[\frac{2^5}{2} = 2^4\]
anonymous
  • anonymous
Does this work with other numbers? \[3^3 = 27\] \[\frac{27}{3} =\ ?\]
anonymous
  • anonymous
9
anonymous
  • anonymous
And 9 is \(3^2\)
anonymous
  • anonymous
Lets see if we can figure out why this might be happening.
anonymous
  • anonymous
What is \(a^2\)
anonymous
  • anonymous
Or better still, \(a^3\)
anonymous
  • anonymous
a*a*a
anonymous
  • anonymous
Ok, now if we have \[\frac{a\cdot a\cdot a}{a}\] We can cancel one of the a's on top with the a on the bottom. So what would that equal?
anonymous
  • anonymous
a^2
anonymous
  • anonymous
Right. So now, coming back to the original question.. What is \[\frac{s^5}{s}\]
anonymous
  • anonymous
5
anonymous
  • anonymous
no.
anonymous
  • anonymous
then just s
anonymous
  • anonymous
What was \[\frac{a^3}{a}\] again?
anonymous
  • anonymous
a*a*a
anonymous
  • anonymous
No, you just said it 6 mins ago. just scroll up
anonymous
  • anonymous
a^2
anonymous
  • anonymous
And do you remember why?
anonymous
  • anonymous
because we cancel out 1
anonymous
  • anonymous
So now. What is \[\frac{s^5}{s}\] Use the same argument as before
anonymous
  • anonymous
s^4
anonymous
  • anonymous
yes, precisely.
anonymous
  • anonymous
So if we divide s^5 by s, we get s^4
anonymous
  • anonymous
And if we divide s^3 by s?
anonymous
  • anonymous
s^2
anonymous
  • anonymous
And if we divide s by s?
anonymous
  • anonymous
s
anonymous
  • anonymous
s/s = s?
anonymous
  • anonymous
What is 2/2
anonymous
  • anonymous
1
anonymous
  • anonymous
What is 5/5
anonymous
  • anonymous
1
anonymous
  • anonymous
And w/w?
anonymous
  • anonymous
w
anonymous
  • anonymous
Why was 5/5 = 1?
anonymous
  • anonymous
s/s=1
anonymous
  • anonymous
why?
anonymous
  • anonymous
s goes into s 1 time
anonymous
  • anonymous
that's a good reason.
anonymous
  • anonymous
So now.
anonymous
  • anonymous
thats why i said s i thought instead of putting 1 you put the variable
anonymous
  • anonymous
If we need to factor an s from s^5 +4s^3 - 8s what will our expression be?
anonymous
  • anonymous
s^4+s^2-8
anonymous
  • anonymous
not quite.
anonymous
  • anonymous
But very close!
anonymous
  • anonymous
i hate this math
anonymous
  • anonymous
\[s^5 + 4s^3 - 8s\]
anonymous
  • anonymous
factor out an s, does that effect the numbers out in front?
anonymous
  • anonymous
no
anonymous
  • anonymous
so where'd the 4 go when you factored?
anonymous
  • anonymous
s(s^4+4s^2-8-5)?
anonymous
  • anonymous
Where'd that 5 come from?
anonymous
  • anonymous
the original equation
anonymous
  • anonymous
jumped the gun a bit
anonymous
  • anonymous
That 5 didn't have an s
anonymous
  • anonymous
So we cannot factor a s from it
anonymous
  • anonymous
no
anonymous
  • anonymous
Our original expression is \[4( s^5 + 4s^3 -8s -5)\] And you said that \[s^5 + 4s^3 -8s = s(s^4 + 4s^2 -8)\] Right?
anonymous
  • anonymous
yes what happens to the 5
anonymous
  • anonymous
We leave it alone. We are going to replace \[s^5 + 4s^3 -8s\] in the original expression with \[s(s^4 + 4s^2 -8)\] What does it look like?
anonymous
  • anonymous
?
anonymous
  • anonymous
What is the original equation (after we factored out the 4)
anonymous
  • anonymous
4(s^5+4s^3-8s-5)
anonymous
  • anonymous
Right. So now take all those terms with an s, and replace them with the factored form you found.
anonymous
  • anonymous
s(s^4+4s^2-8)-5
anonymous
  • anonymous
Where'd the 4 out front go?
anonymous
  • anonymous
4(s^4+4s^2-8)-5
anonymous
  • anonymous
No. Take a second. Look at the original equation \[4(s^5+4s^3-8s-5)\] I want you to retype this equation with a [ and a ] around the terms with an s.
anonymous
  • anonymous
[4(s^5+4s^3-8s]-5)
anonymous
  • anonymous
hrm. I think there's a vocab problem
anonymous
  • anonymous
what is a term?
anonymous
  • anonymous
each number 4s^5
anonymous
  • anonymous
close, but not quite
anonymous
  • anonymous
I realize this has been a very lengthy process, but bear with me for a min
anonymous
  • anonymous
im really bad at math
anonymous
  • anonymous
I want you to know. You can be very good at math. You have the skills. You are a very hard worker clearly.
anonymous
  • anonymous
What is your goal?
anonymous
  • anonymous
it just doesnt make sense to me
anonymous
  • anonymous
I know that, but it's not for the reasons you think.
anonymous
  • anonymous
Somewhere a long time ago, you were learning math. And there were other classes, and due dates, or other life events, and somewhere along the way you missed something here and there. Not a lot, just a little bit. But it was a little bit here, and a little bit there, and slowly over time these little bits add up. They are not hard things to learn. But now you are expected to know them and they are holes in your knowlege. And these holes are making it 100 times harder to learn this new material.
anonymous
  • anonymous
So lets fill a few holes quickly
anonymous
  • anonymous
do you mind?
anonymous
  • anonymous
I promise it will make math less hard
anonymous
  • anonymous
And I assume that you have a reason for taking the math classes you are taking
anonymous
  • anonymous
and don't want to give up on those goals
anonymous
  • anonymous
Believe me. You can learn this.
anonymous
  • anonymous
im majoring in acct
anonymous
  • anonymous
That's awsome!
anonymous
  • anonymous
i drop out in 9th grade got my GED and somehow passed the math test
anonymous
  • anonymous
12yrs ago i dropped out and got GED 1yr ago
anonymous
  • anonymous
Sounds like my story ;)
anonymous
  • anonymous
Except I graduated, but not with terribly good grades. Then screwed around for 15 years before finally going back to school
anonymous
  • anonymous
i had my son dropped out and raised him and had my daughter and dont want to wait anymore
anonymous
  • anonymous
That's good!
anonymous
  • anonymous
yeah so how do i make this easier
anonymous
  • anonymous
So lets learn some math. =)
anonymous
  • anonymous
Starting with vocabulary
anonymous
  • anonymous
Vocabulary is important, because that way when I say something you can know exactly what I mean.
anonymous
  • anonymous
can we finish the problem we were working on first so i can close my homework this is the last problem
anonymous
  • anonymous
I was trying to.
anonymous
  • anonymous
But you weren't understanding what I was saying
anonymous
  • anonymous
k
anonymous
  • anonymous
So vocabulary.
anonymous
  • anonymous
First off, we have a sum. This is a sum: a + b + c
anonymous
  • anonymous
Very simple I know
anonymous
  • anonymous
right
anonymous
  • anonymous
This sum has how many terms?
anonymous
  • anonymous
A term is just the things you are summing together.
anonymous
  • anonymous
How many terms are in the sum: a+b+c ?
anonymous
  • anonymous
3
anonymous
  • anonymous
And how many terms are in the sum a*b + c +d*e
anonymous
  • anonymous
4
anonymous
  • anonymous
How many different things are we adding together?
anonymous
  • anonymous
a*b+c c+d*e so 2?
anonymous
  • anonymous
(a*b) + (c) + (d*e)
anonymous
  • anonymous
so 3
anonymous
  • anonymous
Yes. There are 3 things being added together. Those things are called terms.
anonymous
  • anonymous
Now this is a product: a*b
anonymous
  • anonymous
right
anonymous
  • anonymous
What are the factors of this product?
anonymous
  • anonymous
a b
anonymous
  • anonymous
So how many factors are there?
anonymous
  • anonymous
2
anonymous
  • anonymous
Ok now 5 - 3a + 8c Is that a product, or a sum?
anonymous
  • anonymous
difference of a sum
anonymous
  • anonymous
I'd rather say it was a sum with one negative term
anonymous
  • anonymous
How many terms are in this sum?
anonymous
  • anonymous
2
anonymous
  • anonymous
How many different things are being added (and subtracted) together?
anonymous
  • anonymous
5-3a 3a+8c
anonymous
  • anonymous
Why do you keep breaking it up with repeated parts?
anonymous
  • anonymous
Is 5 - 3 + 2 = 5 - 3 and 3+2 ?
anonymous
  • anonymous
no
anonymous
  • anonymous
So what do you mean 5-3a 3a + 8c ?
anonymous
  • anonymous
5 - 3 + 2 Has how many terms?
anonymous
  • anonymous
2
anonymous
  • anonymous
(5) - (3) + (2)
anonymous
  • anonymous
Or if you prefer (5) + (-3) + (2)
anonymous
  • anonymous
How many things are being added together?
anonymous
  • anonymous
3
anonymous
  • anonymous
yes
anonymous
  • anonymous
5 - 4 + 2 + 6
anonymous
  • anonymous
How many terms?
anonymous
  • anonymous
so each number is a term
anonymous
  • anonymous
no, each thing you are adding together as part of the sum is a term
anonymous
  • anonymous
a + b + c Has no numbers, but still has 3 terms
anonymous
  • anonymous
so 4a+6b+8c is 3 or 6 terms
anonymous
  • anonymous
3 terms.
anonymous
  • anonymous
k
anonymous
  • anonymous
But! 4*3c + 7b + 4*12*7a Also has 3 terms
anonymous
  • anonymous
What is the second term of the above expression?
anonymous
  • anonymous
7b
anonymous
  • anonymous
right.
anonymous
  • anonymous
Ok, now going back to products
anonymous
  • anonymous
7b is a product
anonymous
  • anonymous
you know that 7b is the same as 7*b yes?
anonymous
  • anonymous
I think you're being trolled...
anonymous
  • anonymous
yes or 7(b)
anonymous
  • anonymous
Yes, exactly
anonymous
  • anonymous
Ok, so how many factors are in the product 7b?
anonymous
  • anonymous
2
anonymous
  • anonymous
good
anonymous
  • anonymous
Ok, so what is \(7bc^2\) a sum, or a product?
anonymous
  • anonymous
product
anonymous
  • anonymous
Ok, here's a trickier one. 4(a + 3) Sum or a product?
anonymous
  • anonymous
sum
anonymous
  • anonymous
If I tell you that b = a+3 Wouldn't that expression be 4b ?
anonymous
  • anonymous
is 4b a sum or a product?
anonymous
  • anonymous
product
anonymous
  • anonymous
If 4b is a product, then 4(a+3) must be a product, cause they're basically the same expression
anonymous
  • anonymous
ok
anonymous
  • anonymous
So if 4b is a product, what are its factors?
anonymous
  • anonymous
3,1
anonymous
  • anonymous
No. The factors of 4b are 4, and b
anonymous
  • anonymous
oh yeah sry
anonymous
  • anonymous
So if b = a+3 What are the factors of the product 4(a+3)
anonymous
  • anonymous
a 3
anonymous
  • anonymous
What are the factors of 4b again?
anonymous
  • anonymous
4 b
anonymous
  • anonymous
Ok, in the expression (the product) 4(a+3) What are the factors (things being multiplied together to form the product)?
anonymous
  • anonymous
4 a 4 3
anonymous
  • anonymous
No.
anonymous
  • anonymous
4(a+3) is 4 times (a+3) What two things are being multiplied!!?
anonymous
  • anonymous
4 (a+3)
anonymous
  • anonymous
yes
anonymous
  • anonymous
The product 4(a+3) has 2 factors. They are 4 and (a+3)
anonymous
  • anonymous
One of those factors is a sum. Which one is a sum?
anonymous
  • anonymous
(a+3)
anonymous
  • anonymous
What are the terms of the sum (a+3)
anonymous
  • anonymous
a 3
anonymous
  • anonymous
Correct
anonymous
  • anonymous
Lets try this one
anonymous
  • anonymous
(x+1)(x-2) A product? or a sum?
anonymous
  • anonymous
(x+1) sum (x-2) difference
anonymous
  • anonymous
no.
anonymous
  • anonymous
It is a product. (x+1)(x-2) is (x+1) TIMES (x-2) It is two things multiplied together.
anonymous
  • anonymous
oh ok i get it
anonymous
  • anonymous
Each of those two things by themselves is a sum, but when you multiply them together it's a product.
anonymous
  • anonymous
What is 4(s^5 + 4s^3 - 8s -5) A product? or a sum?
anonymous
  • anonymous
product
anonymous
  • anonymous
yay!
anonymous
  • anonymous
What are the factors of this product?
anonymous
  • anonymous
4 s^5+4s^3-8s-5
anonymous
  • anonymous
yes!
anonymous
  • anonymous
Now, the second factor has many terms with s in them
anonymous
  • anonymous
I want you to find each term with a factor of s
anonymous
  • anonymous
s^5 4s^3 8s
anonymous
  • anonymous
Yes, now. Factor an s out of each of those terms, this will make a product where one factor is an s, and the other factor is the sum of the terms that you took the s from.
anonymous
  • anonymous
s+4^3-8
anonymous
  • anonymous
I'm not sure where to begin there. You were doing well up until that point, so something about my instructions must not have made sense.
anonymous
  • anonymous
i just dont understand what you mean
anonymous
  • anonymous
4 + 16 + 12 Factor a 4 from each of those terms.
anonymous
  • anonymous
4(1+4+3)
anonymous
  • anonymous
yes! perfect
anonymous
  • anonymous
4a + 3a + 2a Factor an a from each of those terms
anonymous
  • anonymous
a(4+3+2)^3
anonymous
  • anonymous
What is the ^3 for?
anonymous
  • anonymous
Why didn't you do the same thing you did for the 4?
anonymous
  • anonymous
i thought for the a's
anonymous
  • anonymous
It wasn't 4(1+4+3)^3
anonymous
  • anonymous
Just put an 'a' out front, and then divide each term by a.
anonymous
  • anonymous
ok
anonymous
  • anonymous
So what is it?
anonymous
  • anonymous
s(^5 +4^3-8)
anonymous
  • anonymous
No. We went over this before. s^5 divided by s is?
anonymous
  • anonymous
s^4
anonymous
  • anonymous
s(s^4+4s^2-8)
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Now take the terms in the original equation that you factored that s from, and put square brackets [] around them
anonymous
  • anonymous
[4(s^4+4s^3-8s-5]
anonymous
  • anonymous
a) that is not the original equation b) the 4 out front is not one of the terms you took an s from
anonymous
  • anonymous
If you do not understand the instructions why don't you ask to clarify?
anonymous
  • anonymous
4s^5+16s^3-32s-20 this is original equation where do i put the brackets i got s from all except the -20
anonymous
  • anonymous
That is a very well thought out question. Thank you. I would like you to go to the form of the expression where we factored out the 4 already. Then place the brackets such that they surround ONLY the terms (from the sum) that you took the s from, and no others.
anonymous
  • anonymous
Realize that you haven't actually factored the s out yet. I just want you do denote which terms you will be taking the s from by placing them in the brackets
anonymous
  • anonymous
s(s^4+4s^2-8) this is where i factored the s
anonymous
  • anonymous
just guessing is [4+4][2-8] the answer you are looking for?
anonymous
  • anonymous
Ok This is the expression I want you to work with: \[4(s^5 + 4s^3 - 8s -5)\] Put square brackets around the terms that have s in them
anonymous
  • anonymous
4([s^5+4s^3-8s]-5)
anonymous
  • anonymous
yes!
anonymous
  • anonymous
Now, do you agree that s^5+4s^3-8s = s(s^4 + 4s^3 - 8) And that s^5+4s^3-8s is what is inside the brackets?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Good. Then delete what is inside the brackets and replace it with the version where the s is factored out. You should not change anything not inside the brackets.
anonymous
  • anonymous
Bah!
anonymous
  • anonymous
You didn't check my work ;p I made a mistake
anonymous
  • anonymous
It should be s(s^4 + 4s^2 - 8)
anonymous
  • anonymous
I had a 3 on the power of the middle term.
anonymous
  • anonymous
4([s^4+4s^2-8]-5)
anonymous
  • anonymous
where'd the s out in front go?
anonymous
  • anonymous
4s([s^4+4s^2-8]-5)
anonymous
  • anonymous
you changed something outside the brackets
anonymous
  • anonymous
so then explain where im suppose to put the s that was in front
anonymous
  • anonymous
Exactly where it was in the factored version. s(s^4 + 4s^2 -8)
anonymous
  • anonymous
4(s[s^4+4s^2-8]-5)
anonymous
  • anonymous
Delete what's in the brackets. Take that whole expression, and put it in the brackets instead.
anonymous
  • anonymous
Sure, that is at least correct.
anonymous
  • anonymous
If you want, you can switch the brackets to parenthesis.
anonymous
  • anonymous
is that the right answer
anonymous
  • anonymous
almost. We still have more we can factor.
anonymous
  • anonymous
\[4(s (s^4 + 4s^2 - 8) - 5)\] There are two terms that have an \(s^2\)
anonymous
  • anonymous
4(s[s^4 + 4s^2 -8)]-5) is this what it should look like with the brackets
anonymous
  • anonymous
yes, except for the ) after the 8
anonymous
  • anonymous
sry forgot to take that out
anonymous
  • anonymous
Which two terms in this expression have an s still?
anonymous
  • anonymous
s^4 s^2
anonymous
  • anonymous
s^4 and 4s^2
anonymous
  • anonymous
The 4 is part of the term
anonymous
  • anonymous
yes forgot the 4
anonymous
  • anonymous
Ok, so you can factor an s^2 from each of those terms s^4 + 4s^2 = s^2( ? + ? )
anonymous
  • anonymous
show me
anonymous
  • anonymous
How did you factor out the 4, or the s, or anything else you've factored so far?
anonymous
  • anonymous
2(s^2+4
anonymous
  • anonymous
I can only assume you made some typos there, but you meant to have s^2(s^2 + 4)
anonymous
  • anonymous
yes ty
anonymous
  • anonymous
Ok, so replace those two terms (ONLY) with the newly factored version of the expression
anonymous
  • anonymous
The two terms in the big expression we are working on.
anonymous
  • anonymous
4(s[s^2+4-8]-5)
anonymous
  • anonymous
where did the s^2 out in front go?
anonymous
  • anonymous
And the parenthases?
anonymous
  • anonymous
s^4 + 4s^3 = s^2(s^2 + 4) So take this [s^4 + 4s^3] and put in this [s^2(s^2 + 4)]
anonymous
  • anonymous
Err I miss typed that exponent again, but you know what I mean.
anonymous
  • anonymous
s^4 + 4s^2 = s^2(s^2 + 4) Take out [ s^4 + 4s^2 ] Put in [ s^2(s^2 + 4) ]
anonymous
  • anonymous
4(s[s^2(s^2 + 4) -8]-5)
anonymous
  • anonymous
yes. exactly. the end.
anonymous
  • anonymous
There are no terms that have any common factors, so we cannot factor anything else out anywhere.
anonymous
  • anonymous
4(s[s^2(s^2 + 4) -8]-5) this is the final answer
anonymous
  • anonymous
Yes. Now I'm going to go do my math homework and go to bed before I have to get up in 5 hours.
anonymous
  • anonymous
i typed in the answer we came up with and it is wrong the answer is 4(s^5+4s^3-8s-5) i had that 2 and 1/2 hrs ago
anonymous
  • anonymous
That's the problem with having a computer grade. The form we came up with is correct. You can factor it a lot of different ways. But "Factor" doesn't make it clear which bits to factor, or how far to factor.
anonymous
  • anonymous
At a minimum the instructions should have been to factor using the greatest common factor.
anonymous
  • anonymous
then at least you would know that the factorization you wanted would include all those terms.
anonymous
  • anonymous
and also you learned a lot more about factoring from the extra practice.
anonymous
  • anonymous
yes i did ty for everything

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