Can Someone Teach Me How to Factor? I'll Invite you to my iPad Contest.. :)

- anonymous

Can Someone Teach Me How to Factor? I'll Invite you to my iPad Contest.. :)

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- schrodinger

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- amistre64

teach? dunno.... I can explain tho :)

- anonymous

it's like this:\[2x^2+3x-3=0\] kind of like foiling.

- amistre64

Yes, the opposite of foiling, the unfoiling if you will...

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## More answers

- anonymous

the easy way?

- amistre64

what I do is assume that I can factor and set it up like this:
if there is a number in the front (that 2 there) use it for "a" in the following:
(x ()/a) (x ()/a)

- anonymous

what's () ?

- amistre64

It is just something to fill in with a number we find.

- amistre64

(x ()/2) (x ()/2)
is what I got so far. you with me?

- anonymous

the signs are still invisible, right?

- amistre64

yep, the equation actually tells us how to fill those in, but they are not important in step one.

- anonymous

ok. i'm understanding it a bit more

- amistre64

How is the last term inthe equation made? by addition or multiplication?

- anonymous

i converted sin of theta into X

- amistre64

X is not important yet; but that little (-3) at the end of your equation...how did it get there? was it (a)(b) = -3? or (a)+(b) = (-3)

- anonymous

the full equation from the textbook was:
\[2\sin ^2 \theta+3\cos \theta-3=0\]

- amistre64

we will keep that in mind for later; but fer now, we need to KNOW how that (-3) got created. Was it by multiplication or addition?

- anonymous

it was from the textbook. it asks me to find the exact values in degrees

- amistre64

let me ask it this way; in order to "FOIL" to factors together to create the equation . The last term ther , that (-3) was made by some process. Was it by adding or multiplying.... think how to "unFOIL" this.

- amistre64

(x + y)(x + y) = xx +xy +xy +yy
(x + y)(x + y) = x^2 +2xy +y^2
Is that last term there, that (y^2) made by adding or by multiply 2 numbers together?

- anonymous

umm.. it's plus and minus

- amistre64

y^2 = y+y ?
or
y^2 = y(y) ?
(-3) = 1 + (-3)?
or
(-3) = (1)(-3)?

- anonymous

by unfoiling it, i get:
\[(2\sin \theta- number)(\sin \theta + number)=0\]

- amistre64

I should probably clarify this:
Do you want to know HOW to factor?
or How to use the quadratic formula to find the answers?

- anonymous

yea.

- anonymous

i need to know how to factor the fastest way

- amistre64

the fastest way is to use the quadratic formula to find the solutions to a quadratic(a squared) equation.

- amistre64

quadratic is a fancy name for: the exponent value of "x" in this equation is a "2".

- anonymous

i meant i want to know how to factor. i'm left with those two numbers. which one should i pick.

- amistre64

Ill step you through how I do it :) which works if there are only inegers involved; otherwise, use the quad formula.

- anonymous

allrights~

- amistre64

step1:
multiply the first number and the last number to get your actual value that you need to factor to get 2 numbers.
In this equation I would that would be:
(2)(3) = 6.
That is step 1.

- anonymous

ok

- amistre64

step 2: setup your factoring into (x....()/a)(x.....()/a).
For this equation that would be this:
(x ( /2)) (x ( /2))
That is step 2:

- amistre64

step 3: look at the sign of the last term. In this case we have a (-3).
If the sign is (+); I either need (+)(+) OR (-)(-)
If the sign is (-) I need (+)(-)
this sign of the last number tells me what I am going to use.
In your case (-3) tells me that I am going to use (+)(-)
step three is done.

- amistre64

step 4: What is the sign of the middle term? In this case we have (+3)
This sign tells me that whichever numbers I pick; the largest one is this sign.
If it is a (-) sign on the middle term; the largest number is (-)
If it is a (+) sign on the middle term; the largest number is (+)
In your case here; the sign of the middle term (+3) is (+); my biggest number will be positive.
Step 4 is done.

- amistre64

step 5: fill in what I already know:
(x + ( /2)) (x - (/2))
step 5 is done.

- amistre64

to clarify; in step 5 I used what I knew from YOUR equation that we are using. ok?

- anonymous

ok. i was wondering how to find the numbers. the rest is fine.

- amistre64

step 6: take the number we got back in step 1, or simply wait til now to get it :)
remember we muliplied the first and last terms. (first)(last)
(2)(3) = 6
we factor (6) to get our numbers.
1,6 2,3 Those are all I can get out of it...
None of these will subtract to get (+3)
6-1 = 5
3-2 = 1
There is no way to use this method to factor your ORIGINAL equation. because we cannot get 2 number that work to fill in our missing stuff.
End here and do quad formula.

- anonymous

ahh, i get it now. that's the answer i want. thanks
heres the ipad link: http://on.fb.me/gJlBGl

- amistre64

there are going to be square roots involved; or maybe even no answer. But this method works for any integer value that can be found :)

- anonymous

thanks!

- amistre64

whats an iPad contest?

- anonymous

kinda like a prize award?

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