Construct a polynomial function with the following properties: third degree, 4 is a zero of multiplicity 2, −3 is the only other zero, leading coefficient is 4

Question

i don't understand

 

Answer 1

When you get a problem where they give you the zeros, use the factored form:

 

p(x) = a(x-p)(x-q)(x-r)

 

where a is the leading coefficient and p. q, and r are the given zeros.  If you get a multiplicity of 2, it means that zero appears twice.  For degree 3, you need three factors:

 

p(x) = 4(x-4)(x-4)(x+3) = 4(x-4)²(x+3)

 

If you need to, multiply it out to put it into standard form.