91Ó°ÊÓ

For the following exercises, find the zeros and give the multiplicity of each. $$ f(x)=x^{3}(x-1)^{3}(x+2) $$

For the following exercises, use the given information to find the unknown value. \(y\) varies inversely with the square root of \(x\). When \(x=64,\) then \(y=12 .\) Find \(y\) when \(x=36\).

For the following exercises, use the Rational Zero Theorem to find all real zeros. \(2 x^{3}-3 x^{2}+4 x+3=0\)

For the following exercises, use synthetic division to find the quotient. $$ \left(x^{4}-10 x^{3}+37 x^{2}-60 x+36\right) \div(x-2) $$

For the following exercises, use the vertex \((h, k)\) and a point on the graph \((x, y)\) to find the general form of the equation of the quadratic function. $$ (h, k)=(0,1),(x, y)=(1,0) $$

For the following exercises, find the slant asymptote of the functions. $$ f(x)=\frac{81 x^{2}-18}{3 x-2} $$

For the following exercises, find the inverse of the function and graph both the function and its inverse. $$f(x)=4-x^{2}, x \geq 0$$

For the following exercises, use synthetic division to find the quotient. $$ \left(x^{4}-8 x^{3}+24 x^{2}-32 x+16\right) \div(x-2) $$

For the following exercises, use the vertex \((h, k)\) and a point on the graph \((x, y)\) to find the general form of the equation of the quadratic function. $$ (h, k)=(1,0),(x, y)=(0,1) $$

For the following exercises, use the given information to find the unknown value. \(y\) varies inversely with the cube root of \(x\). When \(x=27,\) then \(y=5 .\) Find \(y\) when \(x=125 .\)