1. Calculate the following by hand or with a calculator a. The roots of P = s4 +95 +33s + 59s +42 b. The roots of P = s +85 +24s + 37s + 20 c. Determine the polynomials P3 P + P: P = P-P P = P x P d. Evaluate P and P2 when s = 2. 2. Calculate by hand or with a calculator the polynomial P = (s+7) (s+8)(s + 3) (s+5)(s +9) (s + 10) 3. Calculate by hand or with a calculate the following transfer functions: 20(s+2)(5+3)(5+6) a. G(S) = s(s+7)(5+9) (s+10) represented as a numerator polynomial divided by a denominator polynomial. $+10s+29s+20 b. G(s); 5*+75 +225 +30s expressed as factors in the numerator divided by factors in the denominator, similar to the form of G(s) in Pre-work 3a. c. G3(S) = G (s) + G(S); G (S) = G (s) G (s); G5(S) = G (s) G (s) expressed as factors divided by factors and expressed as polynomials divided by polynomials. 4. Obtain the state-space representation of the system described by the transfer function T(s) in phase-variable form. where: A = [29], s+2 s3 +35 +4s +1 T(s): 5. Determine the transfer function of the system described by the state-space representation shown below. Show your calculations clearly. X = AX + Bu Y = CX + Du B = = [], C= [01], D = 0 1. Use MATLAB to solve Pre-work Problem 1. 2. Use MATLAB to solve Pre-work Problem 2 using a single MATLAB command. 3. Use MATLAB to solve Pre-work Problem 3. Also, use various combinations of G (s) and G (s) to find G3 (S), G4 (S) and G5(s). Various combinations imply mixing and matching G (s) and G (s) expressed as factors and polynomials. For example, in finding G3 (s) G (s) can be expressed in factored form and G (s) can be expressed in polynomial form. 4. Use MATLAB to solve Pre-work Problem 4. Make sure that the solution is in the phase variable form. 5. Use MATLAB to solve Pre-work Problem 5.