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Mathematics 34 Online
OpenStudy (anonymous):

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?

OpenStudy (amistre64):

to factor means to under multiplication

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

what can we factor out of the first part?

OpenStudy (anonymous):

2?

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

yes and it would b 2x^2 right?

OpenStudy (amistre64):

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

OpenStudy (anonymous):

then you mult.?

OpenStudy (anonymous):

they both have at least XX

OpenStudy (amistre64):

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

OpenStudy (anonymous):

do u divide? woiuld it b 4x?

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

you cant factor bc there is no x with 36

OpenStudy (amistre64):

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

OpenStudy (anonymous):

9 goes into 36 4 times??

OpenStudy (amistre64):

yes; very good :)

OpenStudy (amistre64):

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

OpenStudy (anonymous):

right

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

1?

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

correct

OpenStudy (anonymous):

thank you so much for helping me. :)

OpenStudy (amistre64):

youre welcome; but we got one last step

OpenStudy (anonymous):

ohh

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

x-4

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

thats our answer

OpenStudy (anonymous):

ok, got it :)

OpenStudy (amistre64):

i knew you would ;)

OpenStudy (anonymous):

again, thanx a lot!

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