Polynomials and fractions

9000146710

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

9000146208

Level: 
B
Factor the following expression. \[ \left (2x - 1\right )^{2} -\left (x + 3\right )^{2} \]
\(\left (x - 4\right )\left (3x + 2\right )\)
\(\left (x - 4\right )\left (3x - 2\right )\)
\(\left (x + 4\right )\left (3x + 2\right )\)
\(\left (x + 4\right )\left (3x - 2\right )\)

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. \[ 64x^{6} + 125 \]
\(\left (4x^{2} + 5\right )\left (16x^{4} - 20x^{2} + 25\right )\)
\(\left (4x^{2} - 5\right )\left (16x^{4} + 20x^{2} + 25\right )\)
\(\left (4x^{2} + 5\right )\left (16x^{3} - 20x^{2} + 25\right )\)
\(\left (4x^{2} - 5\right )\left (16x^{3} + 20x^{2} + 25\right )\)