help me solve this! linear factor/roots of polynomial x^2+2x-120?

Question

i need to factor this, get the linear factor, and the roots pleeeeease!!!

thanks for your help guys, soo i know the factors are 10 and 12 but what exactly are the linear factors?? im horrible at math :0(

Answer 1

First, lets list all the factors of 120:

(1,120), (2,60), (3,40), (4,30), (5, 24), (6, 20) (8,15), (10,12)

Ok, since we have +2x, we want to find a factor pair who's difference is 2. We see this works very nicely for 12 and 10. We want a positive 2x so we should have +12, -10. Thus, it can be factored:

(x+12)(x-10)=0

To get the roots, set each factor = 0
(x + 12) = 0
(x - 10) = 0

Solve for x and you get:
x=-12, x=10.

Answer 2

You should recognize the factors since 120 = 10*12, and 10 and 12 differ by 2 (coefficient of the middle term). So the factors are (x + 12)*(x - 10)

Answer 3

put it in the quadratic equation

-b plus or minus the square root of (b^2- 4ac)
Over 2


a=1
b=2
c= -120

so just solve it

-2 +/- the square root of 2-4*1*120

over 2