Whenever you have a polynomial [tex] p(x) [/tex] and you find out that [tex] p(x_0)=0 [/tex], you can conclude that [tex] (x-x_0) [/tex] is a factor of [tex] p(x) [/tex].
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 [tex] x=5 [/tex] and [tex] x = 7 [/tex].
Recalling what we said in the first paragraph, we can deduce that [tex] (x-5) [/tex] and [tex] (x-7) [/tex] 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 [tex] (x-5)(x-7) [/tex]
