Subtract the rational expressions: \[\frac{x}{x + 3} – \frac{2}{x – 3}\]

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

Which is an alternate form of  \( x^4 – y^4 \), creating a polynomial identity?

Which is the system of inequalities representing the constraints shown by shaded regions in the graph? The x-axis and y-axis span from below zero to above 5, with a scale of 5 in increments of 1. A solid red V-shaped function has a sharp vertex at (2,2) and a y-intercept of (0, 4). The triangular area above it is shaded in light red. A dashed blue parabola opens downward, enclosing a white unshaded parabolic region, while the surrounding area is shaded light blue. The parabola has its vertex at a coordinate with x value roughly halfway between 1 and 2 and y value roughly halfway between 0 and 1. It passes through the coordinates (0, negative 2) and (3, negative 2) and extends downward. The red and blue-shaded areas overlap in the upper portion of the graph. The white parabolic region in the lower portion of the graph remains unshaded.

What is the center of the ellipse shown on the graph? The x-axis spans from below negative 2 to just above 4, and the y-axis spans from below negative 4 to just above 2. Both axes have a scale of 2 in increments of 0.5. The ellipse intersects the x-axis at approximately (negative 1.5, 0) and (3.5, 0). It crosses the y-axis at a point slightly below (0, 2) and another slightly above (0, negative 3). The center of the ellipse is located approximately around (1, negative 1), with a major axis of 12 units and minor axis of 8 units.

Divide and simplify: \[\frac{x^2 + x – 6}{x^2 – x – 12} \div \frac{x + 2}{x – 3}\]

Which points are the \( x \)-intercepts of the polynomial function? The x-axis spans from below negative 5 to above 5, and the y-axis spans from below negative10 to 20. The x-axis has a scale of 5 in increments of 1 and the y-axis has a scale of 10 in increments of 2. The green parabola opens upward, with its vertex at approximately (0, negative 9). The curve is symmetric around the y-axis. It crosses the x-axis at (negative 3, 0) and (3, 0), extending out of view at both ends. 

What are the zeros of the polynomial represented by the graph? The x-axis spans from below negative 5 to above 5, and the y-axis spans from below negative 20 to 10. The x-axis has a scale of 5 in increments of 1 and the y-axis has a scale of 10 in increments of 2. The blue parabola opens upward, with its vertex at approximately (negative 0.5, negative 20). The curve is symmetric around the vertical line passing through the vertex. It intersects the y-axis at (0, negative 20). It crosses the x-axis at (negative 5, 0) and (4, 0), extending out of view at both ends. 

When \( f(x) \) is replaced by \( -f(x) \), what is the effect on the graph?

Which of the following is not a possible factor of \( f(x) = x^3 – 4x^2 + 5x – 2 \) using the Rational Root Theorem?