Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
SEND - IN ASSIGNMENT
UNIT 4
Polynomials
ANSWER KEY
Name: _________________________________________
Teacher:________________________________________
School:_________________________________________
Total ______
=
_________%
82
SHOW ALL WORK FOR FULL MARKS
(when possible)
Version 1 2010
Page 1 of 9
Unit 4
Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
1. Sate the degree of the following polynomials.
a) 5x2  6 x5  3x2
5
a) _____________________________
1 mark
b) 7 xy  3xy 2  5x2 y 2
4
b) _____________________________
1 mark
2. Evaluate 3x2  4 y5  3 for x  2 and y   1
19
2) _____________________________
2 marks
3. Simplify the following:
a)
 4x  3
  x  5
5x  8
a) _____________________________
b)
 4 x 2  7 x  2    3x 2  x  5 
2 marks
x2  6 x  3
b) _____________________________
2 marks
c) 4 x  2  x   3  x  7 
4 x 2  5 x  21
c) _____________________________
2 marks
Version 1 2010
Page 2 of 9
Unit 4
Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
d)  x  1 x  2
e)
x2  3 x  2
d) _____________________________
 4x  15x  2
2 marks
20 x 2  3 x  2
e) _____________________________
f) 2  x  3 x  4  4  2x  1 x  2
2 marks
10 x 2  10 x  32
f) _____________________________
g)


2 marks
 2 x  3 4 x 2  5 x  1
8 x 3  22 x 2  17 x  3
g) _____________________________
4. Determine an expression to represent the shaded region below.
x3
2 marks
x6
x5
2x  9
x 2  29 x  39
4) _____________________________
3 marks
Version 1 2010
Page 3 of 9
Unit 4
Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
5. Expand the following and then simplify.
a)
 3x  5  2
9 x 2  30 x  25
a) ____________________________
b)
2 marks
 2x  3 y  2x  3 y 
4 x2  9 y2
b) _____________________________
c) 4  x  1 x  1  4  x  1
2 marks
2
c) _____________________________
8 x  8
d)
3 marks
 2 x  43
8 x 3  48 x 2  96 x  64
d) _____________________________
3 marks
Version 1 2010
Page 4 of 9
Unit 4
Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
6. For the number 24:
a) List all the factors.
1, 2, 3, 4, 6, 8, 12, 24
a) _____________________________
1 mark
b) Write as prime factorization.
23  3
b) _____________________________
1 mark
c) List the prime factors only.
2, 3
c) _____________________________
1 mark
7. Determine the least common multiple of 18 and 24.
72
7) _____________________________
2 marks
8. What is the greatest common factor of 12, 24, 30, 72 ?
6
8) _____________________________
2 marks
9. Determine the greatest common factor of 12 x5 y, 4 x3 y 2 , 6 x2 y 4 .
2x 2 y
9) _____________________________
2 marks
Version 1 2010
Page 5 of 9
Unit 4
Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
10. Factor each of the following completely.
a) 24a6  6a3
6a 3  4a 3  1 
a) _____________________________
2 marks
b) 27 x2 y3  9 x2 y 2  18x3 y 2
9 x2 y2  3 y  1  2 x 
b) _____________________________
2 marks
c) 4 x  3x  1  3x  1
 4 x  1 3 x  1
c) _____________________________
2 marks
d) 2 x  4 x  3xy  6 y
2
 2 x  3 y  x  2
d) _____________________________
2 marks
e) x2  9 x  14
 x  7 x  2
e) _____________________________
2 marks
f) 2a  14a  60
2
2  a  3 a  10 
f) _____________________________
2 marks
g) x2  5xy  36 y 2
 x  4 y  x  9 y 
g) _____________________________
2 marks
h) 3a2  11a  6
 3a  2 a  3
h) _____________________________
2 marks
Version 1 2010
Page 6 of 9
Unit 4
Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
i) 6 x2  5x  4
 3 x  4 2 x  1
i) _____________________________
2 marks
j) 12a2  9ab  30b2
3  4a  5b  a  2b 
j) _____________________________
2 marks
k) 9 x  24 x  16
2
 3 x  4
k) _____________________________
2
2 marks
l) 25x2  60 xy  36 y 2
5x  6 y
l) _____________________________
2
2 marks
m) 1  16a
2
1  4a 1  4a 
m) _____________________________
2 marks
n) 7 x2  28 y 2
7  x  2 y  x  2 y 
n) ____________________________
2 marks
o)
a2
b2

25
49
 a b  a b 
 5  7  5  7 



o) _____________________________
2 marks
Version 1 2010
Page 7 of 9
Unit 4
Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
p) x4  5x2  36
 x  3  x  3   x 2  4 
p) _____________________________
2 marks
11. Find all integers for k for which the following trinomials can be factored.
a) 6 x2  kx  3
17
17
7,  3,  17
a) _____________________________
2 marks
b) 4 x2  kxy  9 y 2
 4 x  y  x  9 y 
 35 y
 4 x  y  x  9 y 
 35 y
5,  9,  16,  35, 0
b) _____________________________
2 marks
Use this Math Tile Legend to answer questions 12 and 13
Version 1 2010
Page 8 of 9
Unit 4
Foundations of Mathematics and Pre-Calculus 10
Unit 4 Send-In Assignment
On-Line Course
12. Which of the following diagrams best represents the expansion of  x  3 x  1 pictorially?
1111
A
12) _______________________
11)
2 marks
13. Moira was asked to factor 6 x2  x  15 and represent it with math tiles.
What additional tiles would she need to represent the total area of the two factors?
B
13) _____________________________
2 marks
Version 1 2010
Page 9 of 9
Unit 4