Question

Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. Explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.

Answer 1

R1 = 2 ohm           R2 = 3 ohm           R3 = 6 ohm           (a)  When R2 and R3 are connected in parallel with R1 in series we get                 1/R = 1/R2 + 1/R3                 g= 1/3 + 1/6                 = 1/2                 Thus, R = 2 ohm                 Resistance in series = R + R1                 = 2 + 2                 = 4 ohm

          (b)  When R1,R2, R3 are connected in parallel we get                 1/R = 1/R1 + 1/R2 + 1/R3                 = 1/2 + 1/3 + 1/6                 = 1 ohm