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Advanced Algebra Module 02 Problem Set

#1 The following expression was simplified by two different students:

(3m3 – 6) – (-2m3 + m2 + 3)

Alexander’s Solution                                                         Katie’s Solution

m3 + m2 – 3                                                                        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.

Advanced Algebra Module 02 Problem Set

#1 The following expression was simplified by two different students:

(3m3 – 6) – (-2m3 + m2 + 3)

Alexander’s Solution                                                         Katie’s Solution

m3 + m2 – 3                                                                        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