Download Math 20 Chapter 2 Exam 2007 Review Answers

Math 20 Chapter 2 Review Answers
(Marks are listed to help you understand the value of questions and the amount of work
that may be required! You should do all these questions on loose-leaf paper and not on this
review.)
A) Multiplication of Polynomials (10 marks)
Multiply each of the following:
1) 3x(x – 3xy) = 3x2 – 9x2y
2) (x + 1)(x – 2) = x2 – 2x – 1x – 2 = x2 – x – 2
(Remember to FOIL!)
3) (x – 3)(x + 3) = x2 + 3x – 3x – 9 = x2 – 9
4) (x – 2)(y + 4) = xy + 4x – 2y – 8
5) (2x + 3)(x – 2) = 2x2 – 4x + 3x – 6 = 2x2 – x – 6
B) Factoring (36 marks)
Fully factor each of the following. (Watch for the GCF. Write PRIME if not factorable.)
1) 6xy + 12xy2 (1 mark)
= 6xy(1 + 2y)
(Look for GCF first)
2) 10x + 10 (2 marks)
= 10(x + 1)
(Don’t forget the factor of one!)
3) x2 – y2
(2 marks)
= (x + y)(x – y)
(Difference of 2 squares!)
4) x2 + 8x + 12 (2 marks)
= (x + 6)(x + 2)
5) x2 – 10x + 25 (2 marks)
= (x – 5)(x – 5) or (x – 5)2
6) x2 + 4x – 1
= PRIME
(2 marks)
7) x2 – 2x – 48 (2 marks)
= (x – 8)(x + 6)
8) 25x2 – 1 (2 marks)
= (5x + 1)(5x – 1)
(Difference of 2 squares!)
9) x + 2xy + z + 2yz (2 marks)
= x(1 + 2y) + z(1 + 2y)
(Grouping type!)
= (1 + 2y)(x + z)
10) 2x2 + 9x + 9 (2 marks)
= (2x + 3)(x + 3)
(Trial and Error type!)
11) 8x2 + 2xy – 3y2 (2 marks)
= (2x – y)(4x + 3y)
(Remember to guess the middle factors eg. 2x4 first)
12) 2x – 4 + 2y – xy (2 marks)
= 2(x – 2) + y(2 – x)
= 2(x – 2) – y(x – 2)
(Notice how the middle sign changed from + to – )
= (x – 2)(2 – y)
13) (x + 1)2 – 4 (2 marks)
= [(x+1) + 2][(x+1) – 2]
= (x + 3)(x – 1)
(More complicated difference of 2 squares type!)
14) 2x2 – 50 (2 marks)
= 2(x2 – 25)
(Factor out a GCF first!)
= 2(x + 5)(x – 5)
15) 9x2 – 30x + 25
(2 marks)
= (3x – 5)(3x – 5)
or
(3x – 5)2
(Perfect Trinomial Square!)
16) x2 + y2
(2 marks)
= PRIME
(Sum of 2 squares is always prime unless it has a GCF!)
17) 8 – 2x – x2
(2 marks)
= (4 + x)(2 – x)
(Always do a quick FOIL check on these types that are backwards!)
18) x8 – y8
(3 marks)
= (x4 + y4)(x4 – y4)
= (x4 + y4)(x2 + y2)(x2 – y2)
= (x4 + y4)(x2 + y2)(x + y)(x – y)
(Multiple Difference of 2 squares in this question!)
C) Using the b2 – 4ac formula, show all your work to tell whether the following trinomials are
factorable or prime. Circle the correct choice. (4 marks)
1) 2x2 – 10x + 8
Factorable or Prime
a = 2 b = -10 c = 8
b2 – 4ac = (-10)2 – 4(2)(8) = 100 – 64 = 36 (Since 36 is perfect, it is FACTORABLE!)
2) 3x2 + 15x – 24
Factorable or Prime
a = 3 b = 15 c = -24
b2 – 4ac = (15)2 – 4(3)(-24)
= 225 + 288 = 513 (Since 513 =22.649…,it is not perfect. It is PRIME!)