Question

How do I use the factor theorem to prove `x-4` must be a factor of `x^2-3x-4`?

Answer 1

See below.

Explanation:

According to factor theorem, if `(x-4)` is a factor then `f(4)` will `=0`

`therefore` let `f(x)=x^2-3x-4`

`f(4) = 4^2-3(4)-4 = 16-12-4`
`=16-16`
`=0`

`therefore (x-4)` is a factor.