Question

x^2 - 2x - 35? fatorise?

Answer 1

x^2 - 2x - 35


x^2 - 7x+5x - 35


(x^2 - 7x)+(5x - 35)


x(x-7)+5(x-7)


(x+5)(x-7)


So x^2 - 2x - 35 completely factors to (x+5)(x-7)

Answer 2

And the way Jim figured that out was "what are the factors of -35 that add up to 2?

Answer 3

and that's because if a quadratic has factors x-a and x-b, then
(x-a)(x-b) = x^2 - (a+b)x + ab.

Hence with your equation

x^2 - 2x - 35

you know that
a+b = 2; and
ab = -35.

Hence we want factors of -35 that add up to 2.

Those factors are +7 and -5.