Chapter 9

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=(x+1)^{4}+3 $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ x^{3}-4 x^{2}+8=0 $$

For Problems 1-10, find \(f(c)\) by (a) evaluating \(f(c)\) directly, and (b) using synthetic division and the remainder theorem. $$ f(n)=2 n^{5}-1 \text { and } c=-2 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(x^{3}+2 x^{2}-7 x+4\right) \div(x-1) $$

For Problems \(1-20\), graph each rational function. Check first for symmetry, and identify the asymptotes. $$ f(x)=\frac{1}{x^{3}+x^{2}-6 x} $$

Graph each of the following rational functions: $$ f(x)=\frac{-3 x}{x+2} $$

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=-x^{5} $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ x^{3}-10 x-12=0 $$

For Problems 1-10, find \(f(c)\) by (a) evaluating \(f(c)\) directly, and (b) using synthetic division and the remainder theorem. $$ f(n)=3 n^{4}-2 n^{3}+4 n-1 \text { and } c=3 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(2 x^{3}-7 x^{2}+2 x+3\right) \div(x-3) $$

For Problems \(1-20\), graph each rational function. Check first for symmetry, and identify the asymptotes. $$ f(x)=\frac{x}{x^{2}+2} $$

Graph each of the following rational functions: $$ f(x)=\frac{-2}{x^{2}-4} $$

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=(x-2)(x+1)(x+3) $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ x^{4}+4 x^{3}-x^{2}-16 x-12=0 $$

For Problems \(11-20\), find \(f(c)\) either by using synthetic division and the remainder theorem or by evaluating \(f(c)\) directly. $$ f(x)=6 x^{5}-3 x^{3}+2 \text { and } c=-1 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(3 x^{3}+8 x^{2}-8\right) \div(x+2) $$

For Problems \(1-20\), graph each rational function. Check first for symmetry, and identify the asymptotes. $$ f(x)=\frac{6 x}{x^{2}+1} $$

Graph each of the following rational functions: $$ f(x)=\frac{1}{x^{2}-1} $$

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=(x-1)(x+1)(x-3) $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ x^{4}-4 x^{3}-7 x^{2}+34 x-24=0 $$

For Problems \(11-20\), find \(f(c)\) either by using synthetic division and the remainder theorem or by evaluating \(f(c)\) directly. $$ f(x)=-4 x^{4}+x^{3}-2 x^{2}-5 \text { and } c=2 $$

For Problems \(1-20\), graph each rational function. Check first for symmetry, and identify the asymptotes. $$ f(x)=\frac{-4 x}{x^{2}+1} $$

Graph each of the following rational functions: $$ f(x)=\frac{3}{(x+2)(x-4)} $$

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=x(x+2)(2-x) $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ x^{4}+x^{3}-3 x^{2}-17 x-30=0 $$

For Problems \(11-20\), find \(f(c)\) either by using synthetic division and the remainder theorem or by evaluating \(f(c)\) directly. $$ f(x)=2 x^{4}-15 x^{3}-9 x^{2}-2 x-3 \text { and } c=8 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(5 x^{3}-9 x^{2}-3 x-2\right) \div(x-2) $$

For Problems \(1-20\), graph each rational function. Check first for symmetry, and identify the asymptotes. $$ f(x)=\frac{-5 x}{x^{2}+2} $$

Graph each of the following rational functions: $$ f(x)=\frac{-2}{(x+1)(x-2)} $$

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=(x+4)(x+1)(1-x) $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ x^{4}-3 x^{3}+2 x^{2}+2 x-4=0 $$

For Problems \(11-20\), find \(f(c)\) either by using synthetic division and the remainder theorem or by evaluating \(f(c)\) directly. $$ f(x)=x^{4}-8 x^{3}+9 x^{2}-15 x+2 \text { and } c=7 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(x^{3}-6 x^{2}+5 x+14\right) \div(x-4) $$

For Problems \(1-20\), graph each rational function. Check first for symmetry, and identify the asymptotes. $$ f(x)=\frac{x^{2}+2}{x-1} $$

Graph each of the following rational functions: $$ f(x)=\frac{-1}{x^{2}+x-6} $$

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=-x^{2}(x-1)(x+1) $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ x^{3}-x^{2}+x-1=0 $$

For Problems \(11-20\), find \(f(c)\) either by using synthetic division and the remainder theorem or by evaluating \(f(c)\) directly. $$ f(n)=4 n^{7}+3 \text { and } c=3 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(x^{3}+6 x^{2}-8 x+1\right) \div(x+7) $$

For Problems \(1-20\), graph each rational function. Check first for symmetry, and identify the asymptotes. $$ f(x)=\frac{x^{2}-3}{x+1} $$

Graph each of the following rational functions: $$ f(x)=\frac{2}{x^{2}+x-2} $$

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=-x(x+3)(x-2) $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ 6 x^{4}-13 x^{3}-19 x^{2}+12 x=0 $$

For Problems \(11-20\), find \(f(c)\) either by using synthetic division and the remainder theorem or by evaluating \(f(c)\) directly. $$ f(n)=-3 n^{6}-2 \text { and } c=-3 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(2 x^{3}+11 x^{2}-5 x+1\right) \div(x+6) $$

Graph each of the following rational functions: $$ f(x)=\frac{2 x-1}{x} $$

For Problems \(1-22\), graph each of the polynomial functions. $$ f(x)=(2 x-1)(x-2)(x-3) $$

For Problems \(1-20\), use the rational root theorem and the factor theorem to help solve each equation. Be sure that the number of solutions for each equation agrees with Property \(9.3\), taking into account multiplicity of solutions. $$ 2 x^{4}+3 x^{3}-11 x^{2}-9 x+15=0 $$

For Problems \(11-20\), find \(f(c)\) either by using synthetic division and the remainder theorem or by evaluating \(f(c)\) directly. $$ f(n)=3 n^{5}+17 n^{4}-4 n^{3}+10 n^{2}-15 n+13 \text { and } c=-6 $$

Use synthetic division to determine the quotient and remainder for each problem. $$ \left(-x^{3}+7 x^{2}-14 x+6\right) \div(x-3) $$