Suppose you were asked to solve the following two problems on a test. (a) Find the remainder when 3x1000 - 18x562 + 12x + 28 is divided by x + 1. (b) Is x - 1 a factor of x567 - 9x400 + x9 + 27 Obviously, it's impossible to solve these problems by dividing, because the polynomials are of such large degree. Use one or more of the theorems in this section to solve these problems without actually dividing. (a) Find the remainder when 3x1000 18x562 + 12x + 28 is divided by x + 1. (b) Is x - 1 a factor of x567 - 9x400 + x9 + 2? O Yes O No

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