Which are factors of x2 – 4x – 5

Which are factors of x2 – 4x – 5? Check all that apply.
1.) (x – 5)
2.) (x – 4)
3.) (x – 2)
4.) (x + 1)
5.) (x + 5)

The Correct Answer and Explanation is :

The correct answer is: Correct factors of (x^2 – 4x – 5) are: (x – 5) and (x + 1)

To determine the factors of the quadratic expression (x^2 – 4x – 5), we can use the factoring method. The general form of a quadratic equation is given by (ax^2 + bx + c). In our case:

• (a = 1)
• (b = -4)
• (c = -5)

We need to find two numbers that multiply to (ac = 1 \times (-5) = -5) and add up to (b = -4). The numbers that satisfy these conditions are (-5) and (1) because:

[
-5 \times 1 = -5 \quad (\text{product})
]
[
-5 + 1 = -4 \quad (\text{sum})
]

Using these numbers, we can factor the quadratic as follows:

1. Rewrite the middle term ((-4x)) using the two numbers found:
   [
   x^2 – 5x + x – 5
   ]
2. Group the terms:
   [
   (x^2 – 5x) + (x – 5)
   ]
3. Factor out the common factors from each group:
   [
   x(x – 5) + 1(x – 5)
   ]
4. Now, factor out ((x – 5)):
   [
   (x – 5)(x + 1)
   ]

Thus, the expression (x^2 – 4x – 5) factors to ((x – 5)(x + 1)).

Now, we can evaluate the given options to check which are factors:

1. (x – 5): This is a factor, as we found it in our factorization.
2. (x – 4): This is not a factor, as it does not appear in the factorization.
3. (x – 2): This is also not a factor, as it does not appear in the factorization.
4. (x + 1): This is a factor, as it is part of our factorization.
5. (x + 5): This is not a factor, as it does not appear in the factorization.

Correct factors of (x^2 – 4x – 5) are: (x – 5) and (x + 1).