To factor x^2 + 2x - 8 follow these steps
1) Write to factors, with x as the first term, this way:
(x )(x )
2) The sign to the right of the x in the first factor is the same sign of the coeficient of x in the polynomial.
That is +.
The sign to the right of the x of the second factor is the product of the sign of the coefficent of x (this is +) and the sign of the independent term (this is - ).
So that is (+).(-) + -.
Now the two factors have this form:
(x + ) (x - )
3) Now find two numbers whose product is - 8 and whose difference is +2
Those numbers are + 4 and -2.
Then the two factors are:
(x + 4) (x - 2).
So the answer if that the correct factorization is (x + 4) (x - 2)