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.

In Exercises 15–18, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] <IMAGE>

$f\left(x\right)=-x^4+x^2$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=−x²−2x+8

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square of w.

Find the zeros for each polynomial function and give the multiplicity of each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. $f\left(x\right)=-2(x-1)(x+2{)}^2(x+5{)}^3$

Use the graph of the rational function in the figure shown to complete each statement in Exercises 15–20.

As $x\to 1^{+},f\left(x\right)\to$ __

Divide using long division. State the quotient, and the remainder, r(x).$\(\frac{2x^5 - 8x^4 + 2x^3 + x^2}{2x^3 + 1}\)$