Rewrite the equation in standard form and identify the conic:   \(x^2 + y^2 – 8x + 2y + 5 = 0\)

According to the Rational Roots Theorem, what are the possible roots of \( P(x) = 3x^3 + x^2 – 4x – 2 \)?

Simplify the rational expression by factoring: \

How does the graph of \( f(x) = \frac{1}{x + 3} \) differ from \( f(x) = \frac{1}{x} \)?

For \( f(x) = \vert x + 3 \vert \) and \( g(x) = x – 1 \), what is the approximate solution for the system of equations? 

Subtract the following rational expressions: \

Add the following rational expressions: \

If \( x = -3 + 2i \) is a root of a polynomial with real coefficients, what is another root?

Simplify the following: \

Which inequality corresponds to the graph shown? The x-axis spans from negative 2 to 6, and the y-axis spans from below negative 2 to just above 4. Both axes have a scale of 2 in increments of 0.5.   The purple parabola opens downward, with its vertex at (2,1), passing through the y-axis at approximately (0, negative 3) and the coordinate (4, negative 3). It has x intercepts at (1, 0) and (3,0).  The blue V-shaped function is formed by two linear segments that meet at a sharp vertex at (2,1). It extends in opposite directions, with the left segment having a negative slope and the right segment a positive slope. The left segment passes through the point (0,3) and the right segment passes through the point (4,3).  The two graphs intersect at their vertex at (2,1).