graphs of factorable polynomials

1. Graphs of Factorable Polynomials
For example, given two
roots with their orders and
the sign-chart of a
polynomial, the graphs
around each root are as
shown. Connect them to get
the whole graph.
Example C. Given P(x) = -x(x + 2)2(x – 3)2, identify
the roots and their orders. Make the sign-chart.
Sketch the graph about each root. Connect them to
complete the graph.
The roots are x = 0 of order 1, x = -2 of order 2,
and x = 3 of order 2.
+
order=2 order=3

2. Graphs of Factorable Polynomials
The sign-chart of P(x) = -x(x + 2)2(x – 3)2 is
x = -2
order 2
++
x = 0
order 1
x = 3
order 2
By the sign-chart and the order of each root, we draw
the graph about each root. (Note for x = 0 of order 1,
the graph approximates a line going through the point.)
Connect all the pieces to get the graph of P(x).