50 CHAPTER 2. SYSTEMS OF LINEAR EQUATIONS

Those jagged places denote resistors and the numbers next to them give their resis-tance in ohms, written as Ω. The breaks in the lines having one short line and onelong line denote a voltage source which causes the current to flow in the directionwhich goes from the longer of the two lines toward the shorter along the unbrokenpart of the circuit. The current in amps in the four circuits is denoted by I1, I2, I3 andit is understood that the motion is in the counter clockwise direction. If Ik ends upbeing negative, then it just means the current flows in the clockwise direction. ThenKirchhoff’s law states that

The sum of the resistance times the amps in the counter clockwise direction arounda loop equals the sum of the voltage sources in the same direction around the loop.Find I1, I2, I3.

32. Determine whether x3− x2− x+1 and x3− x2 + x−1 are relatively prime. They areobviously not. However, use the technique of partial fractions to verify this or usethe earlier method in an earlier problem for finding the greatest common divisor.