Sign Problems

[SmArTie]

Hi! my name is Bella Sophia. You can call me Bella. Umm in my academy (London Acadmey of Arts and Education) we are just learning factoring trinomials. I have a bit of a predicament. Here is one of the problems.

(im going to use ^ as squared*

x^ - 5x - 14

I got the answer (x-2) (x+7) then x=2 x= -7

The only thing is i dont know what sign to put!

How do i tell whitch sign to put here :?:

x^ - 8x + 15

I know that i have to do this first

(x+ ) (x- )

and then i know that 3x5= 15 and 1x15
or -3x5 or 3x-5 or -1x15 or 1x-15
I know that 5+3= 8 but the 8 in the problem is negative. How do i know which numbers to use?

-3 and 5?
3 and -5?
3 and 5?

 

[galactus]

You would use -3 and -5 because (-3)(-5)=15 and -3-5=-8.

\(\displaystyle x^{2}-8x+15\)

\(\displaystyle x^{2}-3x-5x+15\)

\(\displaystyle (x^{2}-5x)-(3x-15)\)

\(\displaystyle x(x-5)-3(x-5)\)

\(\displaystyle (x-3)(x-5)\)

See, Bella?.

 

[Denis]

(im going to use ^ as squared*
x^ - 5x - 14
I got the answer (x-2) (x+7) then x=2 x= -7
The only thing is i dont know what sign to put!
How do i tell whitch sign to put here :?:

^ is standard typing for "to the power"; so show like this: x^2 - 5x - 14 = 0

How did you get (x-2)(x+7) ? Multiply that out and you get:
x^2 + 7x - 2x - 14 = x^2 + 5x - 14 : should be x^2 - 5x - 14; ok?
So proper factoring:
(x+2)(x-7) = 0
x = -2 or x = 7

Not sure why you have a problem with "what sign to put";
if x+2 = 0, then x = -2 :-2 + 2 = 0
if x-7 = 0, then x = 7 : 7 - 7 = 0
Capish?