Question

I need help understanding how to factor this problem: 5x^6-10x^5-315x^4.
Identify one of the factors. Answer is (x-9)

Answer 1

ok, first notice that every term can be divided by \(x^4\).
so first take out \(x^4\) as a common factor - what do you get?

Answer 2

Im new do i reply here lol sorry

Answer 3

yes - reply here please

Answer 4

5x

Answer 5

that cannot be right.
remember we are factoring out \(x^4\) from \(5x^6-10x^5-315x^4\)

Answer 6

oh so 5x^2

Answer 7

so you should end up with something like:\[x^4(...)\]

Answer 8

there should still be 3 terms within the braces

Answer 9

you have the correct first term

Answer 10

x^4(5x^2-10x-315)?

Answer 11

perfect!
next notice that every term can be divided by 5 - so pull out a 5 from this as well

Answer 12

so divide everything inside by 5 then right?

Answer 13

yes

Answer 14

so you should end up with something like:\[5x^4(...)\]

Answer 15

wait how do i get 5x^4 ? Im sorry if i seem slow

Answer 16

don't worry about being slow - it is finishing the race that is more important! :)

Answer 17

oh wow good words

Answer 18

ok, we originally had x^4(...) and we noticed that every term within the braces is a multiple of 5, so we pulled out a 5 as well to get 5x^4(...)

does that make sense?

Answer 19

oh you mean leave x^2 inside without the 5 and put the 5 infront of x4

Answer 20

yes - that's it

Answer 21

ok let me work on that one sec

Answer 22

one sec im trying to work on dividing

Answer 23

@TheViper JoelPerez89 knows what to do

Answer 24

ok I didn't know sorry :)

Answer 25

np :)

Answer 26

so rewrite it at 5x^4(x^2-10x-315)

Answer 27

you need to divide every term by 5.
you have only divided the first term by 5 here.

Answer 28

made a mistake

Answer 29

try it again please...

Answer 30

ok im frustrated. do I make10x = 2x and 315 = 63?

Answer 31

yes that is correct
and don't worry - take your time :)

Answer 32

5x^4(x^2-2x-63)?

Answer 33

perfect!
now all you need to do is to factor the remaining quadratic inside the braces.

Answer 34

do you know how to do that?

Answer 35

um do you mean 5x^4 ( ? + ?)(? - ?) ?

Answer 36

yes :)

Answer 37

ok let me try. thank your for your help and patience with me

Answer 38

\[5x ^{4}(x+7)(x-9)\]

Answer 39

perfect! you've done it!

Answer 40

wow i cant belive it. You are soo cool lol thank you a bunch

Answer 41

yw - I'm glad I was able to help. :)

Answer 42

if i need more help i just post my problem again right?

Answer 43

Im going to try as many as i can do myself. Its for a test tomorrow.

Answer 44

yes that's right. the usual workflow is:

1. You post a question.
2. One or more people come to your question to help you out.
3. You select the one that best answered your question by clicking on the blue Best Response button next to any one of their replies.
4. You close the question by clicking on the Close button

then the whole process starts again.

Answer 45

ok thanks

Answer 46

one more thing...

Answer 47

yes

Answer 48

if you ever get to stage where you can help someone else out on their question then, if you feel that the person asking the question has put in sufficient effort, you can also award them a medal in the same manner.

Answer 49

oh wow that is great news. If i could help someone i would. Thank you! Did i get you points up for you? I hit best answer

Answer 50

yes - although I am here because I enjoy teaching and learning - I'm not really interested in the medal scheme as such. :)

Answer 51

me too

Answer 52

lol that is great to hear. I dont want answers I just need help understanding. That way I learn the material.

Answer 53

exactly - great attitude! :)

Answer 54

Wow I did the next problem perfectly thanks 2 u. 12y^{5}-9y^{4}+15y^{2} Factored = 3y^{2}(4y^{3}+5)

Answer 55

have you written that out correctly?

Answer 56

um...oh no lol oops

Answer 57

3y^2(4y^3-3y^2+5) :D There

Answer 58

thats it! :)