1. ## factoring trigonometry

Hello,

question is
solve x

3csc^2x-5cscx-2

from what i know to factor this out i need to find the products of -6 that will add up to -5.

so -2*3=-6

-6*1=-6
-6+1=-5

but this doesnt work, can anyone tell me whats the factor form of this and how u got it. I tried using the quadratic eqn but my book got the exact answer!

2. Originally Posted by jepal
Hello,

question is
solve x

3csc^2x-5cscx-2

from what i know to factor this out i need to find the products of -6 that will add up to -5.

so -2*3=-6

-6*1=-6
-6+1=-5

but this doesnt work, can anyone tell me whats the factor form of this and how u got it. I tried using the quadratic eqn but my book got the exact answer!
$\displaystyle 3x^2-5x-2=(3x+1)(x-2)$

3. Originally Posted by TheEmptySet
$\displaystyle 3x^2-5x-2=(3x+1)(x-2)$
ok that works but 1, and -2 doestn add up to -5 or multply to give -6? how did u get this? so confused!!!

4. Originally Posted by jepal
ok that works but 1, and -2 doestn add up to -5 or multply to give -6? how did u get this? so confused!!!
To learn how to multiply polynomials, try here.

Once you have learned the basics, you should be able to confirm the factorization you were given, by multiplying it back together:

Code:
multiplication:
3x + 1
*   x - 2
-------------
-6x - 2
3x^2 + 1x
-------------
3x^2 - 5x - 2
By the way, you will probably want to learn how to factor trinomials, too.

5. u
Originally Posted by stapel
To learn how to multiply polynomials, try here.

Once you have learned the basics, you should be able to confirm the factorization you were given, by multiplying it back together:

Code:
multiplication:
3x + 1
*   x - 2
-------------
-6x - 2
3x^2 + 1x
-------------
3x^2 - 5x - 2
By the way, you will probably want to learn how to factor trinomials, too.
ok. i know how to multiply polynomials and factoring, but it seems that the rules provided by ur links dosnt apply to this one as the factors that multiply to -6 and adds up to -5 is -6, +1. i still dont get how u got -1 and 2. what am i missing here.?

6. Originally Posted by jepal
i know how to multiply polynomials and factoring, but...the factors that multiply to -6 and adds up to -5 is -6, +1. i still dont get how u got -1 and 2. what am i missing here.?
Since you haven't shown your work, I'm afraid it isn't possible to explain where you're having trouble...? Sorry!

You say that you understand that the numbers to use are -6 and +1, so the quadratic gets restated as 3x^2 - 6x + 1x - 2, and then you understand how to factor as 3x(x - 2) + 1(x - 2) = (x - 2)(3x + 1). But then you say you don't understand how to get (x - 2)(3x + 1)...?

Please reply with clarification regarding the point (in the computations above) at which the process stops making sense. Thank you!

7. omg! im really sorry i figured it out now, i forgot about grouping to factor.

So basically what i was doing was:

original equation: 3x^2-5x-2
factors are -6, 1
(3x+ ) (x- )
(3x- 6) (3x+1) obviously doesnt work! for some reason i just always thought that u can just plug in the number without grouping. Lol! I should really review factoring!!