Investigating Polynomial Behavior - Multiplicities

Factors =  $2,\ x^4,\ and\ \left(x-1\right)$  

Set each factor with a variable equal to 0

 $Solve\ x^4=0$  

 $x=0\ with\ multiplicity\ 4$  .... The graph BOUNCES off 0

 $Solve\ x-1=0$  

 $x=1\ with\ multiplicity\ 1$  ... The graph CROSSES at 1

Factors =  $-6,\ x,\ and\ \left(x+1\right)^5$  

Set each factor with a variable equal to 0

 $Solve\ x=0$  

 $x=0\ multiplicity\ 1$  .... The graph CROSSES at 0

 $Solve\ x+1=0$  

 $x=-1\ multiplicity\ 5$  ... The graph WIGGLES at -1

Factors =  $3,\ x,\ \left(x-1\right)^3,\ and\ \left(x+1\right)^2$  

 $Solve\ x=0$  

 $x=0\ multiplicity\ 1$  .... The graph CROSSES at 0

 $Solve\ x-1=0$  

 $x=1\ multiplicity\ 3$  ... The graph WIGGLES at 1

 $Solve\ x+1=0$  

 $x=-1\ multiplicity\ 2$  ... The graph BOUNCES at -1