91Ó°ÊÓ

Graph each polynomial function. Factor first if the expression is not in factored form. Use the rational zeros theorem as necessary. \(f(x)=3 x^{4}+5 x^{3}-2 x^{2}\)

Graph each polynomial function. Factor first if the expression is not in factored form. Use the rational zeros theorem as necessary. \(f(x)=2 x^{3}\left(x^{2}-4\right)(x-1)\)

Use synthetic division to determine whether the given number is a zero of the polynomial function. $$ -5 ; \quad f(x)=x^{3}+7 x^{2}+10 x $$

Find a polynomial function \(f(x)\) of degree 3 with only real coefficients that satisfies the given conditions. Zeros of \(-3,1,\) and \(4 ; \quad f(2)=30\)

Graph each polynomial function. Factor first if the expression is not in factored form. Use the rational zeros theorem as necessary. \(f(x)=x^{2}(x-3)^{3}(x+1)\)

Find a polynomial function \(f(x)\) of degree 3 with only real coefficients that satisfies the given conditions. Zeros of \(-2,-1,\) and \(4 ; \quad f(2)=48\)

Use synthetic division to determine whether the given number is a zero of the polynomial function. $$ -2 ; \quad f(x)=x^{3}-7 x^{2}-18 x $$

Use synthetic division to determine whether the given number is a zero of the polynomial function. $$ \frac{2}{5} ; \quad f(x)=5 x^{4}+2 x^{3}-x+15 $$

Graph each polynomial function. Factor first if the expression is not in factored form. Use the rational zeros theorem as necessary. \(f(x)=2 x^{3}-5 x^{2}-x+6\)

Graph each rational function. $$f(x)=\frac{x^{2}+1}{x}$$