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. $5x\le 2-3x^2$

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>

$f\left(x\right)=(x-3{)}^2$

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.

In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. x³−2x²−11x+12=0

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

Divide using synthetic division. (2x²+x−10)÷(x−2)

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

As $x\to -2^{+},f\left(x\right)\to$ __