x^2 + x - 6 how can i factor it out?

Question

how can i factor this out?
explanation would be helpful.

Answer 1

(x-2)(x+3)

Answer 2

standard factor form is
(ax+A) (bx+B)
since X^2 has no constant in front a and b are 1
(x+A)(x+B)
since -6 is negative either A or B is negative, and the other is positive. assume it's B
(x+A)(x-B)
since the constant in front x is +1, Ax - Bx is 1, meaning A is 1 more than the abs value of B. also, AxB is 6. Just by intuition these two restrictions are met by 3 and -2.
(x+3)(x-2) = x^2+x-6
there you go

Answer 3

(x+3)(x-2)list the factors of 6:1x6 and 2x3 since 6 is negative, 1 of the numbers has to be negative and one has to be positive(negative x positive= negative) then take the factors and plug them into the equation and use process of elimination to find which ones will give u the right equation(i know thats confusing sorry its hard to show ur work on a computer)

Answer 4

(x + 3).(x - 2)
Check
x.(x - 2) + 3.(x - 2)
= x² - 2x + 3x - 6
= x² + x - 6

Answer 5

x^2 + x - 6
= x^2 + 3x - 2x - 6
= x*(x+3) - 2*(x+3)
= (x-2)*(x+3) ....final Answer