Question

What are the factors of x2 – 4x – 5? Check all that apply. x – 5 x – 2 x – 1 x + 1 x + 2 x + 5

Answer 1

its x-5 and x+1

Explanation:

just did it and got it right

Answer 2

1.
`x^(2) -4x-5` is a 2nd degree polynomial, so if it can be factorize, it can be factorized into two 1st degree polynomials:


`x^(2) -4x-5=(x-a)(x-b)`

2. consider the factorized expression. If we factorized back we would get:


`(x-a)(x-b)=xx-bx-ax+ab= x^(2) -(a+b)x+ab`

3. So
`x^(2) -4x-5=x^(2) -(a+b)x+ab`

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
`x^(2) -4x-5=(x-a)(x-b)=(x-5)(x-(-1))=(x-5)(x+1)`

5. The factors are x-5 and x+1