Math 131
EXAM 1
Spring 2012
Write the set described using the roster method.
1) {x|x is a natural number less than 8 and greater than - 8}
1, 2, 3, 4, 5, 6, 7
Use the roster method to list all the elements of set B that are of the indicated type.
0
-7
-6
, 0.4, 3i,
}
2) B = {13, 6, -8, 2.7, 0, - , 9, , -4,
9
0
-9
Nonnegative Rational numbers that are not integers
2 . 7, 0 . 4,
-6
-9
Use the the given value as part of an example to illustrate the indicated property.
3) - 14x ; inverse property of addition
-14x + 14x = 0
Provide an appropriate response.
4) Give an example of a fourth degree trinomial.
x4 + 2x - 6
Determine whether the algebraic expression is a polynomial. If it is a polynomial, determine the degree. If the
polynomial is a monomial, binomial, or trinomial, so state. If the expression is not a polynomial, indicate why not.
3
5) 3x 7 + x 5 - 2x - 2
8
not a polynomial because of the negative exponent
Simplify the polynomial by adding or subtracting, as indicated. Express your answer as a single polynomial in
descending order.
2 4 3 2 4
2
5
1
5
8 3
x - x - x - 8 x2 - x + 9x 4 +
x + 12 - (-x 3 - 6x 5 + 1)
6)
3
4
9
9
6
4
6
15
2 4 3 2 4
16 2 20
15 4 4 3
x - x - xx +
x+2+
x + x + 10 + x 3 + 6x 5 - 1
3
4
9
9
3
2
9
4
45 4 4 3 9 3 27 2 64 2 60
4
6x 5 + x 4 +
x + x + x x x +
x - x + 2 + 10 + - 1
6
6
9
9
36
36
9
9
6x 5 +
49 4 13 3 91 2 56
x +
x x +
x + 11
6
9
36
9
1
Find the product of the polynomials.
7) [8y + (4x + 3)][8y - (4x + 3)]
64y2 - (4x + 3)2
64y2 - 16x 2 + 24x + 9
64y2 - 16x 2 - 24x - 9
8) [(5x - 3) - 6y] 2
[(5x - 3)]2 - 12y(5x - 3) + 36y2
5x 2 - 30x + 9 - 60xy + 36y + 36y2
Divide and simplify.
-4x6 + 32x 5 - 6x
9)
-16x 5
-4x 6
32x 5
- 6x
+
+
-16x 5
-16x 5 -16x 5
x
3
-2+
4
8x4
Divide using long division. Write the final answer below your work.
4x 5 - 6x 4 + 3x 2 - 11x - 10
14x - 40
= 2x 3 - 3x 2 + 5x - 6 +
10)
2
2x - 5
2x 2 - 5
2x 3 - 3x 2 + 5x - 6
2x 2 - 5 4x 5 - 6x 4
+ 3x2 - 11x - 10
- 4x 5
- 10x 3
- 6x 4 + 10x 3 + 3x 2
- - 6x 4
+ 15x 2
10x 3 - 12x 2 - 11x
- 10x 3
- 25x
- 12x2 + 14x - 10
- - 12x2
+ 30
14x - 40
2
Factor the polynomial completely. If the polynomial cannot be factored, say it is prime.
11) 12x 7 + 8x 4 - 15x
x 12x6 + 8x 3 - 15
x 2x 3 + 3 6x 3 - 5
12) 16y2 - 49x 2 - 70x - 25
16y2 - 49x 2 + 70x + 25
16y2 - 7x + 5 2
4y - 7x + 5 4y + 7x + 5
4y - 7x - 5 4y + 7x + 5
13) 16x 6 (a - 3) + 54y9 (3 - a)
16x 6 (a - 3) - 54y9 (a - 3)
2(a - 3) 8x 6 - 27y9
2(a - 3) 2x 2 - 3y3 4x 4 + 6x 2 y3 - 9y6
14) 9x 5 + 9x
9x x 4 + 1
15) x4 + 6x 3 + 8x + 48
x3 x + 6 + 8 x + 6
x + 6 x3 + 8
x + 6 x + 2 x 2 - 2x + 4
3