Math 125
Exam 3
Solve the system by graphing. If the system is inconsistent or dependent, then indicate so.
1) 6x + y = 24
x + 2y = -7
6x + y = 24
y = - 6x + 24
x + 2y = - 7
1
m=2
-7
, 0 = -7, 0
1
5, - 6
2) 7x + 12= 4y - 2
7x = 4y
7x + 12= 4y - 2
7x - 4y = - 14
m=-
7
7
=
-4 4
- 14
, 0 = - 2, 0
7
7x = 4y
7
x=y
4
inconsistent
Solve the system by substitution. If the system is inconsistent or dependent, then indicate so.
3) 8 = 6y - x
9x - 7y = 22
8 = 6y - x
x = 6y - 8
9 6y - 8 - 7y = 22
54y - 72 - 7y = 22
47y = 94
y=2
x = 6 2 - 8 = 12 - 8 = 4
4, 2
Solve the system using the addition method. If the system is inconsistent or dependent, then indicate so.
4) 8x + 5y = -48
6x - 3y = -36
3 8x + 5y = - 48 3
5 6x - 3y = - 36 5
24x + 15y = - 144
30x - 15y = - 180
54x
x=- 6
= - 324
6 - 6 - 3y = - 36
- 36 - 3y = - 36
- 3y = 0
y=0
- 6, 0
Solve the system using the substitution or addition method. If the system is inconsistent or dependent, then indicate so.
3
1
5) x - y = -18
2
3
3
2
x + y = -9
4
9
3
1
x - y = -18 6
2
3
6
36
3
2
x + y = -9 36
4
9
9x - 2y = - 108
27x + 8y = - 324
4 9x - 2y = - 108 4
27x + 8y = - 324
36x - 8y = - 432
27x + 8y = - 324
63x
= - 756
x = - 12
9 - 12 - 2y = - 108
- 108 - 2y = - 108
- 2y = 0
y=0
- 12, 0
Provide an appropriate response.
6) Give an example of a sixth degree trinomial.
x6 + x + 1
Evaluate the polynomial or polynomial function for the given value of the variable.
7) 5x 3 - 4x 2 + 20 for x = -2
5 - 2 3 - 4 - 2 2 + 20
5 - 8 - 4 4 + 20
- 40 - 16 + 20
- 56 + 20
- 36
Simplify.
8) (5x 8 + 4x 7 - 5x 6 - 6) - (3x 8 - 6x 4 + 9x 3 - 2x+ 11) - (- 2x 6 - 3x 3 + 8x 2 - 2x) + (4x 7 + 5x 5 - 6x 4 + 4x 3 )
2x 8 + 8x 7 - 3x 6 + 5x 5 - 2x 3 - 8x 2 + 4x - 17
Provide an appropriate response.
9) Determine the degree of the answer from question 8.
8 is the degree
Find the product.
10) (7y - 6)(49y2 + 42y + 36)
343y3 + 294y2 + 252y - 294y2 - 252y - 216
343y3 - 216
11) (2x + 9)(2x - 9)
4x 2 - 81
12) (6x - 5y) 2
36x 2 - 60xy + 25y2
Divide. Assume all variables are nonzero.
30x 4 + 5x 3 + 35x 2 + 25x - 15
13)
15x
30x 4
5x3
35x 2 25x
15
+
+
+
15x
15x
15x
15x 15x
2x 3 +
x2
7x 5 1
+
+ 3
3
3 x
Divide using long division.
12x 3 - 7x 2 - 28x + 12
24
= 3x 2 - 4x - 4 +
14)
4x + 3
4x + 3
15)
x 3 + 125
= x 2 - 5x + 25
x+5