How do you factor?

x² + 5x - 6
= x² + 6x - x - 6 **
= x(x+6) - 1(x+6)
= (x-1)(x+6)

** Note that:
6+(-1) = 5
6×(-1) = -6

x² + 5x - 6

x² - x + 6x - 6

x(x - 1) + 6(x - 1)

(x - 1)(x + 6)

the factor is (x + 6) ( x -1)

Well, look at it. What two numbers when multiplied give -6 and when added give 5? 6 and -1, so your factors are (x+6)(x-1).

x^2 + 5x - 6
= (x - 1)(x + 6)

You could factor this a few ways, i will use Complete the Square method:
x^2 + 5x - 6

First, you want a perfect square, so take (b/(2a))^2, then add and subtract it. (since it is in the form of ax^2 + bx + c, a = 1, b = 5, and c = - 6)
(b / (2a))^2
(5 / (2*1))^2
(5/2)^2

x^2 + 5x - 6
x^2 + 5x - 6 + (5/2)^2 - (5/2)^2

because "(5/2)^2 - (5/2)^2 = 0", you are not chaning the value of the equation at all.

x^2 + 5x + (5/2)^2 - 6 - (5/2)^2

You now have a perfect square in the first three terms:
(x + 5/2)^2 - 6 - (5/2)^2

Now, combine the last two terms:
(x + 5/2)^2 - 49/4
(x + 5/2)^2 - (7/2)^2

It is now the difference of two squares, which fits a common formula: a^2 - b^2 = (a - b) (a + b), so use that:

( (x + 5/2) - (7/2) ) ( (x + 5/2) + (7/2) )
( x + 5/2 - 7/2) (x + 5/2 + 7/2)
(x - 2/2) (x + 12/2)
(x - 1) (x + 6)

So, the factored form is: (x - 1) (x + 6)