9514 1404 393
Answer:
g(x) = (x -3)(x -2+√7)(x -2 -√7)
Explanation:
Synthetic division can tell us the quadratic factor that remains when the factor (x-3) is divided out.
g(x) = (x -3)(x^2 -4x -3)
The quadratic is not factorable over integers. Its vertex form is ...
(x -2)^2 -7
so its roots are x = 2±√7.
That means the linear factorization of g(x) is ...
g(x) = (x -3)(x -2-√7)(x -2+√7)
_____
I find it easy to learn the vertex form of the quadratic factor by using a graphing calculator to show the graph of the quadratic.