Question

Which are factors of x2 – 4x – 5? Check all that apply.

Answer 1

1.) (x-5) and 4.) (x+1). Factoring works as follows: x*x = x^2 and x*1=x and -5*x=-5x and -5*1=-5. So you then have, x^2+x+(-5x)+(-5), therefore, you get the original: x^2-4x-5. This is how factoring works. You could not have x-4 or x-3 for various reasons, including the fact that the only factors of 5 are 5 and 1.

Answer 2

We have been given a quadratic formula. we need to find the factors. the factors are multiplied by each other and gives rise to the quadratic formula
x² - 4x - 5
to find the factors we need to multiply x² by -5 = -5x²
then the factors of 5x² should add up to -4x. 
possible factors of 5x² are 1x and 5x. 
to get a negative product one factor should be positive and other factor should be negative. the sum of the factors is -4x, then the larger factor should be negative. 
From 1x and 5x, larger factor is 5x therefore it should be -5x.
sum of 1x and -5x is -4x.
we write -4x in the quadratic formula as (1x - 5x)
x² + 1x - 5x - 5
taking the common factors out
x (x + 1) - 5 (x + 1)
(x-5) (x+1)
therefore factors are (x -5) and (x + 1)
answers are 1) and 4)