Hi all, I just need answers for all questions, thanks !

Pre-work: 1. Calculate the following by hand or with a calculator a. The roots of P, = s* + 9s#+ 33s + 59s + 42 b. The roots of P2 = s* + 8s' + 24s' + 37s + 20 c. Determine the polynomials P3 = P1 + P2; P. = P -P, :P, = P, XP2 d. Evaluate Pi 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: a. G(s) = 20(5+2)(s+3)(s+6) s(s+7)(s+9)(5+10) represented as a numerator polynomial divided by a denominator polynomial. b. G2(s) = = $3 +105 +295+20 $4+753+2252+30s expressed as factors in the numerator divided by factors in the denominator, similar to the form of Gi(s) in Pre-work 3a. C. G3 (s) = G1(s) + G2($); GA(s) = G1(s) - G2(s); Gs(s) = G1(s) G2(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. s + 2 T(S) =3+ 352 + 45 + 1 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 where : A=[2 1. B = [. C =10 1], D=0