C

2010001306

Level: 
C
Factor the following polynomial. \[ x^{8} - 1 \]
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + 1\right )\left (x^{4} + 1\right )\)
\(\left (x - 1\right )^2\left (x + 1\right )^2\left (x^{2} + 1\right )^2\)
\(\left (x - 1\right )\left (x + 1\right )\left (x^{3} + 1\right )^2\)
\(\left (x - 1\right )^2\left (x + 1\right )^2\left (x^{4} + 1\right )\)

2010000904

Level: 
C
Assuming \(x\in \mathbb{R}\setminus \left \{-\frac{2} {3}\right \}\), find the quotient of the polynomials: \[ (x^{2} - x - 1) : (3x + 2) \]
\(\frac{1} {3}x -\frac{5} {9} + \frac{\frac{1} {9} } {3x+2}\)
\(\frac{1} {3}x -\frac{5} {9} - \frac{\frac{19} {9} } {3x+2}\)
\(\frac{1} {3}x -\frac{1} {9} + \frac{\frac{7} {9} } {3x+2}\)
\(\frac{1} {3}x -\frac{1} {9} - \frac{\frac{11} {9} } {3x+2}\)

2010000903

Level: 
C
Assuming \(x\in \mathbb{R}\setminus \left \{\pm 1\right \}\), find the quotient of the polynomials: \[ (-3x^{4} + 2x^{2} -4) : (x^{2} + 1) \]
\(- 3x^{2} + 5 - \frac{9} {x^{2}+1}\)
\(- 3x^{2} - 5 - \frac{9} {x^{2}+1}\)
\(- 3x^{2} + 5 +\frac{1} {x^{2}+1}\)
\(- 3x^{2} - 5 +\frac{1} {x^{2}+1}\)

2010000805

Level: 
C
In a parallel circuit the total resistance \( R \) of three components with the resistances \( R_1 \), \( R_2 \), \( R_3 \) is given by the formula \( \frac1R=\frac1{R_1}+\frac1{R_2}+\frac1{R_3} \). Express \( R_2 \) from this formula.
\( R_2=\frac{RR_1R_3}{R_1R_3-R(R_1+R_3)} \)
\( R_2=\frac{R-R_1-R_3}{RR_1R_3} \)
\( R_2=R-\frac{R_1R_3}{R_1+R_3} \)
\( R_2=\frac{R_1R_3-R(R_1+R_3)}{RR_1R_3} \)