Solve each polynomial equation.

$$x^3-2 x^2-48 x=0$$

Solve each polynomial equation. If a solution occurs more than once, state its multiplicity.

$$-2 x^5+24 x^4-70 x^3=0$$

Determine the symmetries of each equation. Then use the properties of symmetry to graph each equation.

$$y=|x-2|$$

Determine the symmetries of each equation. Then use the properties of symmetry to graph each equation.

$$x y^2-1$$

Find the smallest positive integral value for $x$ that makes the following true:

$$\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{x}}}}}>1.4$$

Determine the axis of symmetry, the vertex, and the $x$ - and $y$-intercepts of each quadratic function. Graph each function.

$f(x)=-3 x^2+3$

Determine the remainder on dividing $x^4+x^3+x^4+x^2+x+1$ by $x-1$.

For each point, determine another point that satisfies the specified symmetry.

$(-3,9) ; y$-axis

Factor completely: $25 x^2+50 x y+25 y^2$

Show that $P(-3,2), Q(-2,-1), R(0,3)$, and $S(-1,6)$ are vertices of a parallelogram.

Solve each quadratic equation by factoring.

$$x^2-16 x+55=0$$

Find the slope of the line that passes through the points $(-2,5)$ and $(-6,-4)$.

Express the equation of the given line in the form $A x+B y+C=0$. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

$$x=3 ; P(5,7)$$

Solve.

$$-\frac{42}{y}=\frac{y-25}{3}$$