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?

Question

amistre64 · Answer

to factor means to under multiplication

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

what can we factor out of the first part?

anonymous · Answer

2?

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

yes and it would b 2x^2
right?

amistre64 · Answer

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

anonymous · Answer

then you mult.?

anonymous · Answer

they both have at least XX

amistre64 · Answer

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

anonymous · Answer

do u divide?
woiuld it b 4x?

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

you cant factor bc there is no x with 36

amistre64 · Answer

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

anonymous · Answer

9 goes into 36 4 times??

amistre64 · Answer

yes; very good :)

amistre64 · Answer

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 · Answer

right

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

1?

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

$$2x^2(x−4)+9(-x+4)$$
$$2x^2(x−4)+9(-1)(x-4)$$
$$2x^2(x−4)-9(x-4)$$

amistre64 · Answer

correct

anonymous · Answer

thank you so much for helping me. :)

amistre64 · Answer

youre welcome; but we got one last step

anonymous · Answer

ohh

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

x-4

amistre64 · Answer

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

amistre64 · Answer

$$(A)(2x^2-9)$$
$$(x-4)(2x^2-9)$$

amistre64 · Answer

thats our answer

anonymous · Answer

ok, got it :)

amistre64 · Answer

i knew you would ;)

anonymous · Answer

again, thanx a lot!