91Ó°ÊÓ

For each polynomial function, find all zeros and their multiplicities. \(f(x)=(7 x-2)^{3}\left(x^{2}+9\right)^{2}\)

For each polynomial function, use the remainder theorem and synthetic division to find \(f(k) .\) $$ f(x)=-x^{3}+8 x^{2}+63 ; \quad k=4 $$

Graph each polynomial function. Factor first if the expression is not in factored form. Use the rational zeros theorem as necessary. \(f(x)=2 x(x-3)(x+2)\)

Find a polynomial function \(f(x)\) of least possible degree with only real coefficients and having the given zeros. \(3+i\) and \(3-i\)

For each polynomial function, use the remainder theorem and synthetic division to find \(f(k) .\) $$ f(x)=x^{3}-4 x^{2}+2 x+1 ; \quad k=-1 $$

For each polynomial function, use the remainder theorem and synthetic division to find \(f(k) .\) $$ f(x)=2 x^{3}-3 x^{2}-5 x+4 ; \quad k=2 $$

Graph each polynomial function. Factor first if the expression is not in factored form. Use the rational zeros theorem as necessary. \(f(x)=x^{2}(x+1)(x-1)\)

Find a polynomial function \(f(x)\) of least possible degree with only real coefficients and having the given zeros. \(7-2 i\) and \(7+2 i\)

For each polynomial function, use the remainder theorem and synthetic division to find \(f(k) .\) $$ f(x)=2 x^{5}-10 x^{3}-19 x^{2} ; \quad k=3 $$

Graph each polynomial function. Factor first if the expression is not in factored form. Use the rational zeros theorem as necessary. \(f(x)=x^{2}(x-2)(x+3)^{2}\)