Simplify: \[\frac{x + 2}{x – 3} \cdot \frac{x – 3}{x + 2}\]
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Which factor corresponds to the zero at \( x = 3 \)? The x-…
Which factor corresponds to the zero at \( x = 3 \)? The x-axis spans from negative 2 to 6, and the y-axis spans from below negative 10 to above 5. The x-axis has a scale of 2 in increments of 0.5 and the y-axis has a scale of 5 in increments of 1. The green polynomial function has a local minimum around (1, negative 4) and a local maximum around (3, 0). The function starts from positive infinity in the second quadrant, decreases to the local minimum in the fourth quadrant, rises to the local maximum, and then falls again towards negative infinity, extending out of view at both ends.
If \( x = -3 + 2i \) is a root of a polynomial with real coe…
If \( x = -3 + 2i \) is a root of a polynomial with real coefficients, what is another root?
Which of the following functions has an asymptote at \( y =…
Which of the following functions has an asymptote at \( y = 1 \)?
What is the simplified form of \( (5x^2 + 3x + 1) – (2x^2 +…
What is the simplified form of \( (5x^2 + 3x + 1) – (2x^2 + x) \)?
What is the center of the ellipse shown on the graph? The x…
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.
What is the \( y \)-intercept of the polynomial \( f(x) = x^…
What is the \( y \)-intercept of the polynomial \( f(x) = x^4 – 5x^3 + 3x – 7 \)?
Simplify: \[\frac{4x + 6}{x^2 – 1} + \frac{2x}{x^2 – 1}\]
Simplify: \[\frac{4x + 6}{x^2 – 1} + \frac{2x}{x^2 – 1}\]
What is the focus of the parabola given by \( x + \frac{2}{5…
What is the focus of the parabola given by \( x + \frac{2}{5} = \frac{1}{10}(y – 3)^2 \)? The x-axis spans from below zero to just above 15, and the y-axis spans from below negative 5 to just above 15. Both axes have a scale of 5 in increments of 1. The blue parabola has its vertex slightly right of (negative 0.5, 3) in the second quadrant. It opens rightward to the first and fourth quadrants, while passing through the approximate points (12, 14) and (12, negative 8), extending beyond the visible range at both ends.
When dividing \( P(x) = 2x^3 – 5x + 6 \) by \( x + 2 \), the…
When dividing \( P(x) = 2x^3 – 5x + 6 \) by \( x + 2 \), the quotient is: