Math Questions

#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