Chapter 3

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x-4)(x+2)>0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies directly as \(x . y=65\) when \(x=5 .\) Find \(y\) when \(x=12\)

Find the domain of each rational function. $$f(x)=\frac{5 x}{x-4}$$

In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-x^{3}+x^{2}-4 x-4 $$

Determine which functions are polynomial functions. For those that are, identify the degree. $$ f(x)=5 x^{2}+6 x^{3} $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(x^{2}+8 x+15\right) \div(x+5) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x+3)(x-5)>0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies directly as \(x . y=45\) when \(x=5 .\) Find \(y\) when \(x=13\)

Find the domain of each rational function. $$f(x)=\frac{7 x}{x-8}$$

In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-x^{3}+3 x^{2}-6 x-8 $$

Determine which functions are polynomial functions. For those that are, identify the degree. $$ f(x)=7 x^{2}+9 x^{4} $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(x^{2}+3 x-10\right) \div(x-2) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x-7)(x+3) \leq 0 $$

Find the domain of each rational function. $$g(x)=\frac{3 x^{2}}{(x-5)(x+4)}$$

In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-3 x^{4}-11 x^{3}-x^{2}+19 x+6 $$

Determine which functions are polynomial functions. For those that are, identify the degree. $$ g(x)=7 x^{5}-\pi x^{3}+\frac{1}{5} x $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(x^{3}+5 x^{2}+7 x+2\right) \div(x+2) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x+1)(x-7) \leq 0 $$

Find the domain of each rational function. $$g(x)=\frac{2 x^{2}}{(x-2)(x+6)}$$

In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-2 x^{4}+3 x^{3}-11 x^{2}-9 x+15 $$

Determine which functions are polynomial functions. For those that are, identify the degree. $$ g(x)=6 x^{7}+\pi x^{5}+\frac{2}{3} x $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(x^{3}-2 x^{2}-5 x+6\right) \div(x-3) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-5 x+4>0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies directly as \(x\) and inversely as the square of \(z . y=20\) when \(x=50\) and \(z=5 .\) Find \(y\) when \(x=3\) and \(z=6\)

Find the domain of each rational function. $$h(x)=\frac{x+7}{x^{2}-49}$$

In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-4 x^{4}-x^{3}+5 x^{2}-2 x-6 $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(6 x^{3}+7 x^{2}+12 x-5\right) \div(3 x-1) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-4 x+3<0 $$

Find the domain of each rational function. $$h(x)=\frac{x+8}{x^{2}-64}$$

In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-3 x^{4}-11 x^{3}-3 x^{2}-6 x+8 $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(6 x^{3}+17 x^{2}+27 x+20\right) \div(3 x+4) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}+5 x+4>0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies jointly as \(x\) and \(z . y=25\) when \(x=2\) and \(z=5\) Find \(y\) when \(x=8\) and \(z=12\)

Find the domain of each rational function. $$f(x)=\frac{x+7}{x^{2}+49}$$

In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-x^{5}-x^{4}-7 x^{3}+7 x^{2}-12 x-12 $$

Determine which functions are polynomial functions. For those that are, identify the degree. $$ f(x)=x^{2}-3 x^{2}+5 $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(12 x^{2}+x-4\right) \div(3 x-2) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}+x-6>0 $$

Find the domain of each rational function. $$f(x)=\frac{x+8}{x^{2}+64}$$

In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-4 x^{5}-8 x^{4}-x+2 $$

Determine which functions are polynomial functions. For those that are, identify the degree. $$ f(x)=x^{3}-4 x^{2}+7 $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(4 x^{2}-8 x+6\right) \div(2 x-1) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-6 x+9<0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies jointly as \(a\) and \(b\) and inversely as the square root of \(c, y=12\) when \(a=3, b=2,\) and \(c=25 .\) Find \(y\) when \(a=5, b=3,\) and \(c=9\)

In Exercises \(9-16\) a. List all possible rational zeros. b. Use synthetic division to test the possible rational zeros and find an actual zero. c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)-x^{3}+x^{2}-4 x-4 $$

Determine which functions are polynomial functions. For those that are, identify the degree. $$ f(x)=\frac{x^{2}+7}{x^{3}} $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \frac{2 x^{3}+7 x^{2}+9 x-20}{x+3} $$

In Exercises \(9-16,\) find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)-2(x-3)^{2}+1$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-2 x+1>0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies jointly as \(m\) and the square of \(n\) and inversely as \(p\) \(y=15\) when \(m=2, n=1,\) and \(p=6 .\) Find \(y\) when \(m=3, n=4,\) and \(p=10\)