Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

the easy way?

Answer 5

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)

Answer 6

what's () ?

Answer 7

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

Answer 8

(x ()/2) (x ()/2)

is what I got so far. you with me?

Answer 9

the signs are still invisible, right?

Answer 10

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

Answer 11

ok. i'm understanding it a bit more

Answer 12

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

Answer 13

i converted sin of theta into X

Answer 14

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)

Answer 15

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

Answer 16

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?

Answer 17

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

Answer 18

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.

Answer 19

(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?

Answer 20

umm.. it's plus and minus

Answer 21

y^2 = y+y ?

or

y^2 = y(y) ?

(-3) = 1 + (-3)?

or

(-3) = (1)(-3)?

Answer 22

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

Answer 23

I should probably clarify this:

Do you want to know HOW to factor?

or How to use the quadratic formula to find the answers?

Answer 24

yea.

Answer 25

i need to know how to factor the fastest way

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

allrights~

Answer 31

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.

Answer 32

ok

Answer 33

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:

Answer 34

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.

Answer 35

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.

Answer 36

step 5: fill in what I already know:

(x + ( /2)) (x - (/2))

step 5 is done.

Answer 37

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

Answer 38

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

Answer 39

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.

Answer 40

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

Answer 41

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 :)

Answer 42

thanks!

Answer 43

whats an iPad contest?

Answer 44

kinda like a prize award?