Question

Factor x2 – 4x – 5 = 0. WITH ALL STEPS.

Answer 1

x²-4x-5=0

The given equation is quadratic

So we can perform prime factorisation of it.

factors of -5, that add up to give -4 are -5 and 1

therefore replacing -4x by -5x+x

x²-5x+x-5=0

performing factoring by grouping,

(x²-5x)+(x-5)=0

x(x-5)+(x-5)=0

(x+1)(x-5)=0

x+1=0 and x-5=0

Answer is x=-1 and x=5

Answer 2

We must find such numbers, whose sum is equal to -4, and the product is equal to -5.

-4 = 1 + (-5)

-5 = 1 · (-5)

Therefore:

$x^2-4x-5=0\\\\x^2+1x-5x-5=0\\\\x(x+1)-5(x+1)=0\\\\(x+1)(x-5)=0$

The solutions to this equation are numbers: -1 and 5.