Question

Factor
4sˆ5+16s³-32s-20
4s^5 is suppose to be 4s exponent5 but i dont know how to do it

Answer 1

What have you done so far?

Answer 2

nothing

Answer 3

Well, do you know how to find the factors of each term?

Answer 4

cf is 4

Answer 5

That is a start. Pull a factor of 4 from each term and see what you have left.

Answer 6

4, 8, 5

Answer 7

No, I mean write the new expression after you factor out a 4

Answer 8

4(4s^3-8s-5)

Answer 9

Not quite. You're missing a s^5, but otherwise that's good.

Answer 10

Now what other factors do some of your terms have in common?

Answer 11

s

Answer 12

Ok, so factor those out from the terms that have it

Answer 13

not sure how

Answer 14

show me step by step plz and then explain

Answer 15

How did you factor out the 4?

Answer 16

4(4s^3-8s-5)

Answer 17

Right, but I mean what did you do?

Answer 18

Also that's not right

Answer 19

divide each term by 4

Answer 20

You keep forgetting the 4s^5

Answer 21

then what would it be

Answer 22

4(s^5 +4s^3 - 8s - 5)

Answer 23

But as I said, you can factor an s from the first 3 terms inside the parens.

Answer 24

Or rather, like you said.

Answer 25

And you would do it the same way. Put an s out front, and divide each term by the s you took away.

Answer 26

Just don't take one away from the term that doesn't have an s to start with.

Answer 27

s(^5+4^3-8-5)

Answer 28

No. What is \[\frac{s^5}{s}\]

Answer 29

idk im really bad with fractions

Answer 30

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.

Answer 31

Lets start now.

What is \[\frac{32}{2}\]

Answer 32

16

Answer 33

Ok, and if I said

\[\frac{2^5}{2}\]
?

Answer 34

rawr!

Answer 35

a^5

Answer 36

What is \(2^5\)

Answer 37

32

Answer 38

Interesting. And what was \[\frac{32}{2} \] again?

Answer 39

16/1

Answer 40

Right.. Just curious, but what is 2^4?

Answer 41

rawr! rawr!

Answer 42

16

Answer 43

That's interesting.

\[\frac{2^5}{2} = 2^4\]

Answer 44

Does this work with other numbers?
\[3^3 = 27\]
\[\frac{27}{3} =\ ?\]

Answer 45

9

Answer 46

And 9 is \(3^2\)

Answer 47

Lets see if we can figure out why this might be happening.

Answer 48

What is \(a^2\)

Answer 49

Or better still, \(a^3\)

Answer 50

a*a*a

Answer 51

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?

Answer 52

a^2

Answer 53

Right.

So now, coming back to the original question..

What is \[\frac{s^5}{s}\]

Answer 54

5

Answer 55

no.

Answer 56

then just s

Answer 57

What was \[\frac{a^3}{a}\] again?

Answer 58

a*a*a

Answer 59

No, you just said it 6 mins ago. just scroll up

Answer 60

a^2

Answer 61

And do you remember why?

Answer 62

because we cancel out 1

Answer 63

So now. What is \[\frac{s^5}{s}\]
Use the same argument as before

Answer 64

s^4

Answer 65

yes, precisely.

Answer 66

So if we divide s^5 by s, we get s^4

Answer 67

And if we divide s^3 by s?

Answer 68

s^2

Answer 69

And if we divide s by s?

Answer 70

s

Answer 71

s/s = s?

Answer 72

What is 2/2

Answer 73

1

Answer 74

What is 5/5

Answer 75

1

Answer 76

And w/w?

Answer 77

w

Answer 78

Why was 5/5 = 1?

Answer 79

s/s=1

Answer 80

why?

Answer 81

s goes into s 1 time

Answer 82

that's a good reason.

Answer 83

So now.

Answer 84

thats why i said s i thought instead of putting 1 you put the variable

Answer 85

If we need to factor an s from s^5 +4s^3 - 8s what will our expression be?

Answer 86

s^4+s^2-8

Answer 87

not quite.

Answer 88

But very close!

Answer 89

i hate this math

Answer 90

\[s^5 + 4s^3 - 8s\]

Answer 91

factor out an s, does that effect the numbers out in front?

Answer 92

no

Answer 93

so where'd the 4 go when you factored?

Answer 94

s(s^4+4s^2-8-5)?

Answer 95

Where'd that 5 come from?

Answer 96

the original equation

Answer 97

jumped the gun a bit

Answer 98

That 5 didn't have an s