solving quadratic by process of division and finding all roots and then the factors

The equation x - 18x + 121x - 368x + 420=0 has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of : x - 18x + 121x - 368x + 420 Please can you show all working out including the division part of this problem as I would like to understand the process behind this problem for future use. Please see attached.

The problems are from stat class, 400 level course.

a. Test is the difference in lifetime of vehicles exist between the two manufacturers at a=0.01. Please see attached.

Analytic Functions; Harmonic Functions; Laplace's Equation

5. Let the function ... be analytic in a domain D that does not include the origin ... 13. ... state why the functions ... are harmonic in D and why ... is in face, a harmonic conjugate 11. ... Why must this satisfy Laplace's equation? Please see attachment for complete questions. Thanks.

Proving ∑ 1/(n^2) = (Pi^2)/6 using Cauchy's Residue Theorem

Deducing that ∑ 1/(n^2) = (Pi^2)/6 is a classic problem in Mathematics. Often it is demonstrated by using Fourier series, but it can also be proved by using Cauchy's Residue Theorem.

Review: Arc, Cauchy-Goursat Theorem, Integral, Paratmetric Representation etc.

Please assist me with the attached problems, such as: 1. Without evaluating the integral show that (see attachment) when C is the same arc as the one in Example 1 (see attachment for example)