Question

How do you factor and find the zeroes for `P(x)= x^2 - 9`?

Answer 1

The zeros of a function `P(x)` are the values of `x` for which `P(x) = 0`

By the difference of squares:

`color(white)("XXXXX")` `x^2-9 = (x+3)(x-3)`

If `P(x) = 0` then

`color(white)("XXXXX")` `(x+3)(x-3)=0`

which can only be true if

either

`color(white)("XXXXX")` `x=-3` or `x=+3`