Question

How do you factor completely `5x^2-5x-100`?

Answer 1

`5(x-5)(x +4)`

Explanation:

`color(white)(xx)5x^2 - 5x - 100`

`= 5(x^2 - x - 20)` [First take the common part out]

`= 5{x^2 - (5 - 4)x - 20}` [We can write `1` as `(5 - 4)`]

`= 5{x^2 - 5x + 4x - 20}` [Multiply using Distributive Property]

`= 5{x(x - 5) + 4(x - 5)}` [Put the like terms in group]

`= 5(x - 5)(x + 4)` [Group `(x - 5)` terms]

And we got our answer. Hope this helps.