Advanced Algebra Module 02 Problem Set #1 The following expression was simplified by two different students: (3m3 - 6) - (-2m3 + m2 + 3) Alexander's Solution m3 + m2 - 3 Katie's Solution 5m3 - m2 - 9 Which student simplified correctly? Explain how you determined the correct one. #2 Divide (x2 - 3x - 33) (x - 4) . Show ALL your work! #3 The binomial below is squared incorrectly. Explain the mistake and square is correctly. (3x + 7)2 = 9x2 + 49 #4 These binomials are called conjugants: (4x + 1) and (4x -1). In the case of conjugates when they are multiplied the product is a binomial which is the difference of squares. (4x + 1) (4x - 1) = 16x2 - 1 Use the idea of conjugants and given this difference of squares 100x2 - 121 , factor it. #5 The following is an example of factoring a GCF out of a binominal: 45c6 + 54c8 = 9c6(5 + 6c2) First factor out a GCF of ONE of the following binomials and then complete the factoring using the factoring formulas of the sum of cubes or the difference of cubes. 24x3 + 81 or 24x3 - 81