1. [tex]x^{2} -4x-5[/tex] is a 2nd degree polynomial, so if it can be factorize, it can be factorized into two 1st degree polynomials:
[tex] x^{2} -4x-5=(x-a)(x-b)[/tex]
2. consider the factorized expression. If we factorized back we would get:
[tex](x-a)(x-b)=xx-bx-ax+ab= x^{2} -(a+b)x+ab[/tex]
3. So [tex]x^{2} -4x-5=x^{2} -(a+b)x+ab[/tex]
comparing the coefficients, we see that
a+b=4 and ab=-5.
From ab=-5, a is either 5 (b=-1) or a is -5 (b=1). Together with the condition a+b=4, we see that the right choice is a=5 and b=-1
4. so [tex]x^{2} -4x-5=(x-a)(x-b)=(x-5)(x-(-1))=(x-5)(x+1)[/tex]
5. The factors are x-5 and x+1
