91Ó°ÊÓ

For Problems \(35-42\), (a) find the \(y\) intercepts, (b) find the \(x\) intercepts, and (c) find the intervals of \(x\) where \(f(x)>0\) and those where \(f(x)<0\). Do not sketch the graphs. $$ f(x)=x(x-6)^{2}(x+4) $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(9 x^{3}-6 x^{2}+3 x-4\right) \div\left(x-\frac{1}{3}\right) $$

For Problems \(35-44\), use synthetic division to show that \(g(x)\) is a factor of \(f(x)\), and complete the factorization of \(f(x)\). $$ g(x)=x+1, \quad f(x)=x^{3}-2 x^{2}-7 x-4 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(2 x^{3}+3 x^{2}-2 x+3\right) \div\left(x+\frac{1}{2}\right) $$

For Problems \(35-44\), use synthetic division to show that \(g(x)\) is a factor of \(f(x)\), and complete the factorization of \(f(x)\). $$ g(x)=x-5, \quad f(x)=2 x^{3}+x^{2}-61 x+30 $$

For Problems \(35-42\), (a) find the \(y\) intercepts, (b) find the \(x\) intercepts, and (c) find the intervals of \(x\) where \(f(x)>0\) and those where \(f(x)<0\). Do not sketch the graphs. $$ f(x)=(x+2)^{2}(x-1)^{3}(x-2) $$

For Problems \(35-44\), use synthetic division to show that \(g(x)\) is a factor of \(f(x)\), and complete the factorization of \(f(x)\). $$ g(x)=x-6, \quad f(x)=x^{5}-6 x^{4}-16 x+96 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(3 x^{4}-2 x^{3}+5 x^{2}-x-1\right) \div\left(x+\frac{1}{3}\right) $$

For Problems \(35-42\), (a) find the \(y\) intercepts, (b) find the \(x\) intercepts, and (c) find the intervals of \(x\) where \(f(x)>0\) and those where \(f(x)<0\). Do not sketch the graphs. $$ f(x)=x^{2}(2-x)(x+3) $$

Explain what it means to say that the equation \((x+3)^{2}=\) 0 has a solution of \(-3\) with a multiplicity of two.