Question

simplify: 6x^5 -51x^3 -27x

Answer 1

ok - first can you spot the common factor between all three terms?

Answer 2

you could start by just looking at the constants: 6, 51, 27
what number divides into all of these?

Answer 3

3

Answer 4

good, so we can first simplify this as follows:\[6x^5-51x^3-27x=3(2x^5-17x^3-9x)\]do you understand so far?

Answer 5

yes :)

Answer 6

gr8!
so next try and spot what can be factored out of: \(x^5,x^3,x\)
what goes into all of these?

Answer 7

x

Answer 8

good - can you write out what you think the simplification will be when we take a single 'x' outside of the braces?

Answer 9

3x(2x^4 -17x -9)

Answer 10

almost! the 17x should actually be 17x^2

Answer 11

i no I just forgt

Answer 12

:)
ok, you should therefore end up with:\[6x^5-51x^3-27x=3(2x^5-17x^3-9x)=3x(2x^4-17x^2-9)\]which can be simplified further

Answer 13

you should be able to factorise the terms within the braces

Answer 14

think of then as a quadratic equation in \(x^2\)

Answer 15

so if you say let \(z=x^2\) then you would have: \(2z^2-17z-9\)
Can you factorise this?

Answer 16

yes

Answer 17

what do you get?

Answer 18

3x(x-9)(2x+1)

Answer 19

great work! but you need to be careful - remember we substituted \(z=x^2\), so what you've really ended up with is:\[3x(z-9)(2z+1)\]and if we replace z with \(x^2\) now, then we get:\[3x(x^2-9)(2x^2+1)\]

Answer 20

there is one more simplification that can be made - can you spot it?

Answer 21

the squares?

Answer 22

thats it! you're an expert in these I see! :)

Answer 23

haha I'm really not but thx

Answer 24

so what do you do to the squares? just remove them?

Answer 25

no - when you said the squares I assumed you meant the \((x^2-9)\) term.
this is a difference of two squares since it can be written as: \((x^2-3^2)\)

Answer 26

and there is a well know factorisation for this

Answer 27

\[a^2-b^2=(a+b)(a-b)\]

Answer 28

do you understand?

Answer 29

yup= 3x(x+3)(x-3)(2x+1)

Answer 30

remember the LSAT term there should be \((2x^2+1)\)

Answer 31

*LAST

Answer 32

how to I factor that one?

Answer 33

you cannot - you have now simplified as far as possible.

Answer 34

oh ok

Answer 35

so final result should be:\[3x(x+3)(x-3)(2x^2+1)\]

Answer 36

so can you plz write the answer :)

Answer 37

oh ok thx
also since u r a moderator do u get paid for this?

Answer 38

intern?

Answer 39

no :)
I do this as a hobby because I enjoy teaching (and learning) maths

Answer 40

so how did u become a moderator?

Answer 41

this has been asked a lot in the OpenStudy Feedback Group - let me find a link to it for you...

Answer 42

here are a couple:
http://openstudy.com/study#/updates/4ed6f358e4b0bcd98cb19549
http://openstudy.com/study#/updates/4f667f95e4b0f81dfbb475a2