C

9000146710

Level: 
C
Divide the following two polynomials using long division. \[ \left (x^{3} + 3x^{2} - x + 4\right ) : \left (x^{2} - x + 1\right ) \]
\(x + 4 + \frac{2x} {x^{2}-x+1}\)
\(x + 4 + \frac{2x+8} {x^{2}-x+1}\)
\(x + 2 + \frac{6-2x} {x^{2}-x+1}\)
\(x + 2 + \frac{2x+2} {x^{2}-x+1}\)

9000146209

Level: 
C
Factor the following expression. \[ 27a^{3} - 8b^{9} \]
\(\left (3a - 2b^{3}\right )\left (9a^{2} + 6ab^{3} + 4b^{6}\right )\)
\(\left (3a + 2b^{3}\right )\left (9a^{2} - 6ab^{3} + 4b^{6}\right )\)
\(\left (3a - 2b^{3}\right )\left (9a^{2} + 12ab^{3} + 4b^{6}\right )\)
\(\left (3a + 2b^{3}\right )\left (9a^{2} - 12ab^{3} + 4b^{6}\right )\)

9000146210

Level: 
C
Factor the following expression. \[ 64x^{6} + 125 \]
\(\left (4x^{2} + 5\right )\left (16x^{4} - 20x^{2} + 25\right )\)
\(\left (4x^{2} - 5\right )\left (16x^{4} + 20x^{2} + 25\right )\)
\(\left (4x^{2} + 5\right )\left (16x^{3} - 20x^{2} + 25\right )\)
\(\left (4x^{2} - 5\right )\left (16x^{3} + 20x^{2} + 25\right )\)

9000145401

Level: 
C
Identify a true statement on the function \(f(x) = 2x^{3} + 3x^{2} - 12x - 12\).
The function \(f\) has a local maximum at the point \(x = -2\).
The function \(f\) has a local minimum at the point \(x = -2\)..
The global maximum of \(f\) on \(\mathbb{R}\) is at \(x = -2\).
The global minimum of \(f\) on \(\mathbb{R}\) is at \(x = -2\).

9000145402

Level: 
C
Identify a true statement about the function \(f(x) = 2x^{2} -\frac{x^{4}} {4} \).
The global maximum of \(f\) on \(\mathbb{R}\) is at \(x = 2\) and \(x = -2\).
The global minimum of \(f\) on \(\mathbb{R}\) is at \(x = 2\) and \(x = -2\).
The function \(f\) has a local minimum at the point \(x = 2\).
The function \(f\) has a local minimum at the point \(x = -2\).

9000145403

Level: 
C
Identify a true statement on the function \(f(x)= \frac{4-3x} {x\left (1-x\right )}\).
The function \(f\) has a local minimum at the point \(x = \frac{2} {3}\).
The function \(f\) has a local maximum at the point \(x = \frac{2} {3}\).
The global maximum of \(f\) on \(\mathbb{R}\setminus \{0.1\}\) is at \(x = \frac{2} {3}\).
The global minimum of \(f\) on \(\mathbb{R}\setminus \{0.1\}\) is at \(x = \frac{2} {3}\).

9000145404

Level: 
C
Identify a true statement about the function \(f(x) = x^{3} - 3x^{2} + 3x + 2\).
There is neither local minimum nor maximum of \(f\).
The function \(f\) has a local maximum at the point \(x = 1\).
The function \(f\) has a local minimum at the point \(x = 1\).
The global minimum of \(f\) on \(\mathbb{R}\) is at \(x = 1\).

9000145405

Level: 
C
Identify a true statement on the function \(f(x) = \frac{1} {4}x^{4} -\frac{2} {3}x^{3} -\frac{3} {2}x^{2} + 2\text{ on }\left (-2;4\right )\).
The function \(f\) has a local maximum at the point \(x = 0\).
The function \(f\) has a local minimum at the point \(x = 0\).
The global maximum of \(f\) on this interval is at \(x = 0\).
The global minimum of \(f\) on this interval is at \(x = 0\).

9000145406

Level: 
C
Identify a true statement on the function \(f(x) = x^{3} - 12x + 20\text{ on }\left (-3;4\right )\).
The global minimum of \(f\) on this interval is at \(x = 2\).
The global maximum of \(f\) on this interval is at \(x = 2\).
The function \(f\) has a local minimum at the point \(x = -2\).
The global minimum of \(f\) on this interval is at the point \(x = -2\).

9000145407

Level: 
C
Identify a true statement on the function \(f(x) = x^{4} - 8x^{3} + 22x^{2} - 24x + 12\).
The global minimum of \(f\) on \(\mathbb{R}\) is at \(x = 1\) and \(x = 3\).
The global maximum of \(f\) on \(\mathbb{R}\) is at \(x = 2\).
The local minima of \(f\) are at \(x = 1\) and \(x = 2\).
The local maximum of \(f\) is at \(x = 3\).