Download Completely factor the following trinomials.

Name:_________________________ TECM 1303 Activity 4(Due by Mar. 28)
Dear Instructor or Tutor,
These problems are designed to let my students show me what they have learned and what they
are capable of doing on their own. Please allow them to work the problems on their own! If
you would like to help them with similar problems, here are the related homework problems:
pg. 239:#1-31 odd, pg. 245:#1-23 odd, pg. 250:#1-21 odd, pg. 275:#1-41 odd, pg. 278:#1-29
odd, pg. 287:#1-29 odd Thanks!
Graph the following systems of equations. Determine if the system has 1 solution, no solution,
or infinitely many solutions. If the system has one solution, tell what it is.
1.
x  y  10
x  y  10
2.
2 x  3 y  12
4 x  6 y  12
3.
x y7
2 x  2 y  14
4.
4 x  5 y  20
4 x  y  20
5.
7.
x5
y  3
x2
x  3
6.
y  2x
y  3x
8.
y  4x
y4
Solve the following systems using either substitution or elimination. (Show your Steps!)
x  y  10
2 x  3 y  12
9.
10.
x  y  10
4 x  6 y  12
11.
x y7
2 x  2 y  14
12.
x  3y 1
2x  5 y  3
13.
7 x  2 y  19
y  x  13
15.
x  3 y  17
 x  4 y  18
14.
16.
3x  8 y  1
x y2
9 x  2 y  50
3x  4 y  16
17.
2 x  3 y  34
5 x  4 y  7
Solve the following word problems using a system of equations.
18. The sum of two numbers is 30. One number is 2 more than six times the other number.
Find the two numbers.
19. The sum of the digits of a two-digit number is 10. The number is 2 less than eight times the
units digit. Find the number.
20. Lira has $4.80 in nickels and quarters. If she has a total of 52 coins, how many of each kind
of coin does she have?
21. Drew and Piper went to Karl’s Kookie Kommune to buy some cookies. Drew bought 5
chocolate chip and 8 butter cookies for $4.11. Piper bought 7 chocolate chip and 4 butter
cookies for $3.81. What is the cost of each type of cookie?
Completely factor the following polynomials using GCF and/or Difference of Squares.
22. 15x 2  20 x
23. 24 x3 y 2  32 xy 4
24. 5a  x  2   3b  x  2 
25. 4 x 2  x  6   8 x  x  6 
26. x 2  81
27. 9 x 2  16 y 2
28. x 4  16 y 4
29. 5 x3  180 x
30. 2 x5 y 2  162 xy 6
31. 4 x3  16 x
32. x  9 x  20
2
34. x 2  x  30
Completely factor the following trinomials.
33. x 2  11x  18
35. x 2  5 x  6
36. x 2  3x  54
37. 3x2  9 x  30
38. 3x2  3x  36
39. x 4  3x3  18x 2
Completely factor the following polynomials using grouping.
40. xy  6 x  4 y  24
41. xy  8 x  4 y  32
42. 3xy  4 x  3 y  4
43. 3xy  4 y  6 x  8
44. xy  12  2 x  6 y
45. 12 x 2  9 y  27 xy  4 x
46. x3  2 x2  25x  50
47. 48x3  64 x2  3x  4
Bonus#1:
What is it called when a cartoon dog plunges into the water?
Solve each system of equations by graphing. Match the solution with the corresponding letter.
Place this letter in the box with the problem number to get the answer to the riddle.
y  3x
1.
y  13 x
x4
6.
y  2
x  5
2.
y  x3
y  4  2x
7.
yx4
3.
y  x
y  3x  4
8.
y  5x
y  x4
y  x4
y  2x  5
y  2x  3
9.
y  x3
4.
y  2x
y  3x  3
y  2x  1
10.
y  x  1
5.
A  1, 5 
B  0,3
C 1,5 
D  1,1
E  3, 2 
F 10, 6 
G  5, 8
R  1,6 
S  3, 6 
T 1, 2 
U  0, 4 
V  4, 2 
W  6,1
Y  2, 3
H  5,10 
I  0, 0 
5
L  9, 4 
8
7
M  4, 9 
9
10
3
N  1,3
1
6
1
O  8, 4 
4
2
P  3,9 
Bonus#2: Factor each expression. Use the code to learn who was the first woman in space.
E.  x  9  x  9 
1. x 2  4
E.  3x  2  3x  2 
2. x 2  49
T.  x  10  x  10 
3. x 2  100
V.  x  6  x  6 
4. x 2  25
R.  x  4  x  4 
5. x 2  1
N.  x  2  x  2 
6. x 2  9
V.  x  7  x  7 
7. x 2  16
S. 10 x  9 10 x  9 
8. x 2  36
A.  x  5 x  5
9. x 2  64
A.  x  1 x  1
10. x 2  81
T.  x  3 x  3
11. 4 x 2  9
L.  x  8 x  8
12. 9 x 2  4
N. 9  2 x  y  2 x  y 
13. 25 x 2  1
H.  2 x  3 2 x  3
14. 81x 2  4
I.  9 x  2  9 x  2 
15. 49 x 2  16
16. 64 x 2  49
E.  5x  1 5x  1
17. 100 x2  81
18. 36 x 2  9 y 2
K. 8 x  7 8 x  7 
8
6
10
4
9
7
O.  7 x  4  7 x  4 
13
12
1
17
3
14
18
5
11
16
15
2
4
Bonus#3: Factor each trinomial. Use the code to learn the name of the naturalist who is
credited with inventing raisin bread.
O.  x  8 x  5
1. x 2  3x  2
D.  x  14  x  3
2. x 2  5 x  6
E.  x  9  x  6 
3. x 2  13x  40
A.  x  8 x  3
4. x 2  13x  36
N.  x  2  x  1
5. x 2  17 x  42
D.  x  9  x  7 
6. x 2  12 x  35
E.  x  8 x  4 
7. x 2  15x  54
T.  x  5 x  7 
8. x 2  16 x  63
R.  x  5 x  6 
9. x 2  15x  50
V.  x  3 x  2 
10. x 2  11x  30
H.  x  9  x  4 
11. x 2  11x  24
I.  x  26  x  2 
12. x 2  11x  28
U.  x  5 x  10 
13. x 2  11x  18
A.  x  9  x  2 
14. x 2  12 x  32
Y.  x  7  x  4 
15. x 2  28x  52
4
7
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