algebra 2 problem

Question

Can I get some assistance with this

Given the following polynomial, find
a. The zeros and multiplicity of each

b. Where the graph crosses or touches the axis
c. Number of turning points
d. End behavior
f (x) = - (x-3)^2 (x +1)^3 (x-7)

Answer 1

The zeros are obtained by equating the polynomial to 0.  Zeros of a polynomial are the values of the variable in the polynomial (the values of x in this present case) for which the value of the polynomial returns 0.  

 

So we have -(x-3)²(x+1)³(x-7)=0

 

For the expression on the left needs to equal 0, one of the factors must be 0.  This means that the expression on the left is 0 at x=-1, 3 and 7.  The mulitplicity is given by the exponent.  This tells us that the zeros are -1 with a multiplicity of 3, 3 with a multiplicity of 2 and 7 with multiplicity 1.