Download Polynomial Expressions 1

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Generation Date: 02/22/2015
Generated By: Robert Dilliplane
1. Simplify: (4x2 + 2x + 6)(3x - 5)
A. 12x3 - 14x2 + 8x - 30
B. 12x3 - 14x2 + 8x + 30
C. 12x3 - 26x2 + 28x - 30
D. 12x3 + 26x2 + 28x + 30
2. Simplify the following expression.
(2x5 + 9x4 - 17x2 + 30) - (8x5 + 13x4 + 5x2 - 5)
A. -6x5 + 4x4 + 22x2 - 35
B. 10x5 + 22x4 - 12x2 + 25
C. 10x5 - 4x4 + 22x2 - 35
D. -6x5 - 4x4 - 22x2 + 35
3. Simplify: (3x - 9)(6x2 + 9x - 2)
A. 18x3 - 27x2 - 87x - 18
B. 18x3 + 81x2 + 75x - 18
C. 18x3 - 81x2 + 75x + 18
D. 18x3 - 27x2 - 87x + 18
4. Simplify the following expression.
(4x + 3)2
A. 16x2 + 12x + 9
B. 16x2 + 24x + 9
C. 16x2 - 9
D. 16x2 - 24x + 9
5. Simplify the following expression.
(7x2 + 6x - 3) - (4x2 + 7)
A. 11x2 + 6x - 10
B. 11x2 + 6x - 4
C. 3x2 + 6x - 10
D. 4x2 + 9x - 2
6. A polynomial expression is shown below.
ex(2x3 + 4x2 - 6) - (x2 + 5)(x2 + 6)
The expression is simplified to 17x4 + 36x3 - 11x2 - 54x - 30.
What is the value of e?
A. 8
B. 9
C. -9
D. -8
7. Simplify the following expression.
(6x3 + 5x2 + 8) + (-2x3 + 2x - 4)
A. 8x3 + 5x2 + 2x + 12
B. 4x3 + 2x - 4
C. 8x3 + 5x2 + 2x - 12
D. 4x3 + 5x2 + 2x + 4
8. Simplify: (x + 7)(4x2 + 8x + 7)
A. 4x3 + 20x2 + 63x + 49
B. 4x3 + 20x2 - 49x + 49
C. 4x3 + 36x2 + 49x + 49
D. 4x3 + 36x2 + 63x + 49
9. Simplify the following expression.
(7x2 - 5x + 6) + (-2x2 - 7x + 2)
A. 5x2 - 2x + 8
B. 9x2 - 12x + 4
C. 5x2 - 2x - 8
D. 5x2 - 12x + 8
10. A polynomial expression is shown below.
(12x5 - 30x4) - (sx3 - 7)(2x2 - 5x + 2)
The expression is simplified to -12x3 + 14x2 - 35x + 14.
What is the value of s?
A. 6
B. -2
C. -6
D. 2
Answers
1. A
2. D
3. D
4. B
5. C
6. B
7. D
8. D
9. D
10. A
Explanations
1. Since multiplication is commutative, it is easiest to rearrange the problem so that the binomial
(3x - 5) comes before the trinomial (4x2 + 2x + 6).
Now, distribute 3x - 5 across 4x2 + 2x + 6, then combine like terms.
(3x - 5)(4x2 + 2x + 6) = (3x)(4x2) + (3x)(2x) + (3x)(6) + (-5)(4x2) + (-5)(2x) + (-5)(6)
= 12x3 + 6x2 + 18x - 20x2 - 10x - 30
= 12x3 + 6x2 - 20x2 + 18x - 10x - 30
= 12x3 - 14x2 + 8x - 30
2.
(2x5 + 9x4 - 17x2 + 30) - (8x5 + 13x4 + 5x2 - 5).
2x5 + 9x4 - 17x2 + 30 - 8x5 - 13x4 - 5x2 + 5
(2x5 - 8x5) + (9x4 - 13x4) + (-17x2 - 5x2) + (30 + 5)
-6x5 - 4x4 - 22x2 + 35
Distribute the negative.
Combine like terms.
3. Distribute 3x - 9 across 6x2 + 9x - 2, then combine like terms.
(3x - 9)(6x2 + 9x - 2) = (3x)(6x2) + (3x)(9x) + (3x)(-2) + (-9)(6x2) + (-9)(9x) + (-9)(-2)
= 18x3 + 27x2 - 6x - 54x2 - 81x + 18
= 18x3 + 27x2 - 54x2 - 6x - 81x + 18
= 18x3 - 27x2 - 87x + 18
4. Start by writing the expression as a product of two binomials, and then use the FOIL method
(First Outer Inner Last) to multiply the two expressions. Then, combine like terms.
(4x + 3)2 = (4x + 3)(4x + 3)
= 16x2 + 12x + 12x + 9
= 16x2 + 24x + 9
5. Since the expression shows the subtraction of a polynomial, distribute the negative, and then
combine like terms.
(7x2 + 6x - 3) - (4x2 + 7) = 7x2 + 6x - 3 - 4x2 - 7
= (7x2 - 4x2) + (6x) + (-3 - 7)
= 3x2 + 6x - 10
6.
First, set the polynomial expression equal to the simplified expression.
Then, simplify both sides of the equation.
ex(2x3 + 4x2 - 6) - (x2 + 5)(x2 + 6) = 17x4 + 36x3 - 11x2 - 54x - 30
2ex4 + 4ex3 - 6ex - (x4 + 6x2 + 5x2 + 30) = 17x4 + 36x3 - 11x2 - 54x - 30
2ex4 + 4ex3 - 6ex - (x4 + 11x2 + 30) = 17x4 + 36x3 - 11x2 - 54x - 30
2ex4 + 4ex3 - 6ex - x4 - 11x2 - 30 = 17x4 + 36x3 - 11x2 - 54x - 30
(2ex4 - x4) + 4ex3 - 11x2 - 6ex - 30 = 17x4 + 36x3 - 11x2 - 54x - 30
(2e - 1)x4 + 4ex3 - 11x2 - 6ex - 30 = 17x4 + 36x3 - 11x2 - 54x - 30
(2e - 1)x4 + (4e)x3 + (-6e)x = 17x4 + 36x3 - 54x
Next, solve for e.
(2e - 1)x4 = 17x4</td
2e - 1 = 17
2e = 18
e=9
(4e)x3 = 36x3
4e = 36
e=9
(-6e)x = -54x
-6e = -54
e=9
Therefore, the value of e is 9.
7. Since it is addition of two polynomials, drop the parenthesis and collect like terms.
(6x3 + 5x2 + 8) + (-2x3 + 2x - 4) = 6x3 + 5x2 + 8 - 2x3 + 2x - 4
= (6x3 - 2x3) + 5x2 + 2x + (8 - 4)
= 4x3 + 5x2 + 2x + 4
8. Distribute x + 7 across 4x2 + 8x + 7, then combine like terms.
(x + 7)(4x2 + 8x + 7) = (x)(4x2) + (x)(8x) + (x)(7) + (7)(4x2) + (7)(8x) + (7)(7)
= 4x3 + 8x2 + 7x + 28x2 + 56x + 49
= 4x3 + 8x2 + 28x2 + 7x + 56x + 49
= 4x3 + 36x2 + 63x + 49
9. Since it is addition of two polynomials, drop the parentheses and collect like terms.
(7x2 - 5x + 6) + (-2x2 - 7x + 2) = 7x2 - 5x + 6 - 2x2 - 7x + 2
= (7x2 - 2x2) + (-5x - 7x) + (6 + 2)
= 5x2 - 12x + 8
10.
First, set the polynomial expression equal to the simplified expression.
Then, simplify both sides of the equation.
(12x5 - 30x4) - (sx3 - 7)(2x2 - 5x + 2) = -12x3 + 14x2 - 35x + 14
12x5 - 30x4 - (2sx5 - 5sx4 + 2sx3 - 14x2 + 35x - 14) = -12x3 + 14x2 - 35x + 14
12x5 - 30x4 - 2sx5 + 5sx4 - 2sx3 + 14x2 - 35x + 14 = -12x3 + 14x2 - 35x + 14
12x5 - 30x4 - 2sx5 + 5sx4 - 2sx3 = -12x3
(12x5 - 2sx5) + (-30x4 + 5sx4) - 2sx3 = -12x3
(12 - 2s)x5 + (-30 + 5s)x4 + (-2s)x3 = -12x3
Next, solve for s.
(12 - 2s)x5 = 0x5
12 - 2s = 0
-2s = -12
s=6
(-30 + 5s)x4 = 0x4
-30 + 5s = 0
5s = 30
s=6
(-2s)x3 =
12x3
-2s = -12
s=6
Therefore, the value of s is 6.