**Advanced Algebra Module 02 Problem Set**

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

(3m^{3} – 6) –
(-2m^{3} + m^{2} + 3)

Alexander’s Solution Katie’s Solution

m^{3} + m^{2} –
3
5m^{3} - m^{2} – 9

Which student simplified correctly? Explain how you determined
the correct
one.

#2 Divide (x^{2} – 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} = 9x^{2} + 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) = 16x^{2} –
1

Use the idea of conjugants and given
this *difference of squares*
100x^{2} – 121 , factor it.

#5 The following is an example of factoring a GCF out of a binominal:

45c^{6} + 54c^{8} = 9c^{6}(5 +
6c^{2})

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:

(3m^{3} – 6) –
(-2m^{3} + m^{2} + 3)

Alexander’s Solution Katie’s Solution

m^{3} + m^{2} –
3
5m^{3} - m^{2} – 9

Which student simplified correctly? Explain how you determined
the correct
one.

#2 Divide (x^{2} – 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} = 9x^{2} + 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) = 16x^{2} –
1

Use the idea of conjugants and given
this *difference of squares*
100x^{2} – 121 , factor it.

#5 The following is an example of factoring a GCF out of a binominal:

45c^{6} + 54c^{8} = 9c^{6}(5 +
6c^{2})

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.

24x^{3} +
81
or
24x^{3} -
81

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