Question

What does the factor theorem mean?

Answer 1

According to Factor Theorem: If `x=a` satisfies the polynomial `P(x)` i.e. if `x=a` is a root of the polynomial equation `P(x)=0` then `(x-a)` will be a factor of polynomial `P(x)`

Answer 2

See explanation

Explanation:

Suppose you have an equation. For example: `y=x^2-x-12`

In this case if we set `y=0` and substitute `4` for `x` then we have: `y=(4)^2-(4)-12 = 16-4-12 =0`

So if the equation equals 0 `->f(x)=0`

and by substituting `x=4 ->f(4)` we get the answer `f(4)=0`

then by using `(x-4)("something else") ->0("something else")=0`
So `(x-4)` is a factor of `f(x)`