I do not understand how to factor...I know the basics but when we go further I get stuck. Could someone explain to me how to do this problem? ok my book says Factor By Grouping:2x cubed-8x squared-9x+ 36....where do i start?

- anonymous

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- amistre64

to factor means to under multiplication

- amistre64

you have to understand the mechanics of how the quadratic there was formed in order to know how to take it apart

- anonymous

I know I have to find the GCF first
then the same with the exponent

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## More answers

- amistre64

err... thats a cubic lol; math notation helps

- amistre64

2x cubed-8x squared-9x+ 36 notates to:
2^3 -8x^2 -9x +36

- anonymous

lol...i didnt know how to type it in here

- amistre64

first group them; and see if it wroks...
\[(2x^3-8x^2)+(-9x+36)\]

- amistre64

what can we factor out of the first part?

- anonymous

2?

- amistre64

2x^2 (x -4) ; is what i get do you see why?

- amistre64

2 is part of it; but they also have some 'x's in common right?

- anonymous

yes and it would b 2x^2
right?

- amistre64

(2xxx - 8xx) have what in common:
2xx (x-4)

- anonymous

then you mult.?

- anonymous

they both have at least XX

- amistre64

then we see what the other part factors to..
(-9x +36) factor to what?

- anonymous

do u divide?
woiuld it b 4x?

- amistre64

you do the same process as you did in the firs part ..... nothing new is happening here.

- amistre64

lets say its 4x and test that:
4x* ? = -9x ?
4x * ? = 36?

- anonymous

you cant factor bc there is no x with 36

- amistre64

your right; no 'x' factors out; but what do they have in common? not 'what do they have thats not in common'

- anonymous

9 goes into 36 4 times??

- amistre64

yes; very good :)

- amistre64

what we have done so far looks like this right?
\[2x^3 -8x^2 -9x +36\]
\[(2x^3-8x^2)+(-9x+36)\]
\[2x^2(x-4)+9(-x+4)\]

- anonymous

right

- amistre64

but we want those parenthesis to be the same .... and right now they are close, but slightly different right?

- anonymous

right..the 2nd x needs to be positive??

- amistre64

how do we get: (x-4) to equal (-x+4) ? what can we factor out of ...lets say the one on the right?

- anonymous

1?

- amistre64

close, real close; but lets try a (-1)
\[(-x+4)\iff -1(x-4)\]

- anonymous

ohh ok....i always get confused with the negatives...but that would make it a positive and it would be (x-4)?

- amistre64

\[2x^2(x−4)+9(-x+4)\]
\[2x^2(x−4)+9(-1)(x-4)\]
\[2x^2(x−4)-9(x-4)\]

- amistre64

correct

- anonymous

thank you so much for helping me. :)

- amistre64

youre welcome; but we got one last step

- anonymous

ohh

- amistre64

we gotta factor this last part again to get our final answer

- amistre64

\[2x^2(x−4)−9(x−4)\]
what do these have in common that we can factor out?
think of it as:
\[2x^2(A)-9(A)\]

- anonymous

x-4

- amistre64

good :) so lets pull that out and see whats left

- amistre64

\[(A)(2x^2-9)\]
\[(x-4)(2x^2-9)\]

- amistre64

thats our answer

- anonymous

ok, got it :)

- amistre64

i knew you would ;)

- anonymous

again, thanx a lot!

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