Quadratic Factors in Polynomials
Author: John Maharry
Date: 10/11/2010

What does a quadratic factor do to a Polynomial?

The Sliders on the left for "d" and "e" change two of the "zeros" for the graph.
The Sliders for "b" and "c" change the quadractic factor.

What happens when the quadratic factor (and the polynomial) have real zeros?

What happens when you change "c" so the parabola doesn't have any zeros?

How does changing "b" change the shape of the fourth degree polynomial?

Graph of a  Polynomial with Quadratic Factor

f(x) =  ( x² + bx +c )  ( x - d ) ( x - e )

g(x) =  ( x² + bx +c ) 

e = -3 (slider from -5 to 5, step 0.1)
b = -0.6 (slider from -5 to 5, step 0.1)
c = -2 (slider from -5 to 5, step 0.1)
d = 4 (slider from -5 to 5, step 0.1)
E: (e, 0.0)
C: (c, 0.0)
B: (b, 0.0)
D: (d, 0.0)
f(x) = (x^(2.0) + b * x + c) * (x - d) * (x - e)
g(x) = x^(2.0) + b * x + c