Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 3, -2 is the only other zero, leading coefficient is 2.f(x)=?​Can some help?

Accepted Solution

Answer:[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]Step-by-step explanation:we know that2 is a zero of multiplicity 3 of the polynomialsowe have thatx=2  is a solution of the polynomialA factor of the polynomial is[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3and the other solution is x=-2since the polynomial  is fifth degree, x=-2 must have a multiplicity 2sothe other factor of the polynomial is  [tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2thereforeThe polynomial is equal to multiply the factors by the leading coefficientso[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]