Question

What is the factorization??

Answer 1

Whenever you have a polynomial
`p(x)` and you find out that
`p(x_0)=0`, you can conclude that
`(x-x_0)` is a factor of
`p(x)`.

In this case, we have to assume that the graph is a parabola, i.e. a polynomial of degree 2. We can also see where this polynomial equals zero, i.e. where it intersects the x-axis: the two points are
`x=5` and
`x = 7`.

Recalling what we said in the first paragraph, we can deduce that
`(x-5)` and
`(x-7)` are two factors of this parabola. But this means that we found two factors of degree 1 of a polynomial of degree 2, which means that this must be the complete factorization.

So, we can say that this polynomial is factored into
`(x-5)(x-7)`