Final answer:
The quadratic equation e^2 - 4e - 5 can be factored into (e - 5)(e + 1). The two numbers that help accomplish this factorization are -5 and +1, which when multiplied together result in -5 and when added together result in -4.
Step-by-step explanation:
The question asks us to factor the quadratic equation e^2 − 4e − 5. To factor this equation, we look for two numbers that multiply to give the product of the quadratic coefficient (which is 1, since it's not shown) and the constant term (-5) while adding up to the linear coefficient (-4).
These two numbers are -5 and +1 because (-5) * (+1) = -5 and (-5) + (+1) = -4. Thus, the factored form of the equation is (e - 5)(e + 1).
To confirm, we can apply the FOIL method (First, Outer, Inner, Last) to these factors:
First: e * e = e^2
Outer: e * (+1) = +e
Inner: (-5) * e = -5e
Last: (-5) * (+1) = -5
Add them together, and we get back to the original equation: e^2 + e - 5e - 5, which simplifies to e^2 - 4e - 5.