East Stroudsburg Area School District
Study Island
Copyright © 2015 Edmentum - All rights reserved.
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Generation Date: 02/22/2015
Generated By: Robert Dilliplane
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1. Simplify: (4x2 + 2x + 6)(3x - 5)
|[pic|A. |12x3 - 14x2 + 8x - 30 |
|] | | |
|[pic|B. |12x3 - 14x2 + 8x + 30 |
|] | | |
|[pic|C. |12x3 - 26x2 + 28x - 30 |
|] | | |
|[pic|D. |12x3 + 26x2 + 28x + 30 |
|] | | |
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2. Simplify the following expression.
(2x5 + 9x4 - 17x2 + 30) - (8x5 + 13x4 + 5x2 - 5)
|[pic|A. |-6x5 + 4x4 + 22x2 - 35 |
|] | | |
|[pic|B. |10x5 + 22x4 - 12x2 + 25 |
|] | | |
|[pic|C. |10x5 - 4x4 + 22x2 - 35 |
|] | | |
|[pic|D. |-6x5 - 4x4 - 22x2 + 35 |
|] | | |
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3. Simplify: (3x - 9)(6x2 + 9x - 2)
|[pic|A. |18x3 - 27x2 - 87x - 18 |
|] | | |
|[pic|B. |18x3 + 81x2 + 75x - 18 |
|] | | |
|[pic|C. |18x3 - 81x2 + 75x + 18 |
|] | | |
|[pic|D. |18x3 - 27x2 - 87x + 18 |
|] | | |
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4. Simplify the following expression.
(4x + 3)2
|[pic|A. |16x2 + 12x + 9 |
|] | | |
|[pic|B. |16x2 + 24x + 9 |
|] | | |
|[pic|C. |16x2 - 9 |
|] | | |
|[pic|D. |16x2 - 24x + 9 |
|] | | |
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5. Simplify the following expression.
(7x2 + 6x - 3) - (4x2 + 7)
|[pic|A. |11x2 + 6x - 10 |
|] | | |
|[pic|B. |11x2 + 6x - 4 |
|] | | |
|[pic|C. |3x2 + 6x - 10 |
|] | | |
|[pic|D. |4x2 + 9x - 2 |
|] | | |
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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?
|[pic|A. |8 |
|] | | |
|[pic|B. |9 |
|] | | |
|[pic|C. |-9 |
|] | | |
|[pic|D. |-8 |
|] | | |
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7. Simplify the following expression.
(6x3 + 5x2 + 8) + (-2x3 + 2x - 4)
|[pic|A. |8x3 + 5x2 + 2x + 12 |
|] | | |
|[pic|B. |4x3 + 2x - 4 |
|] | | |
|[pic|C. |8x3 + 5x2 + 2x - 12 |
|] | | |
|[pic|D. |4x3 + 5x2 + 2x + 4 |
|] | | |
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8. Simplify: (x + 7)(4x2 + 8x + 7)
|[pic|A. |4x3 + 20x2 + 63x + 49 |
|] | | |
|[pic|B. |4x3 + 20x2 - 49x + 49 |
|] | | |
|[pic|C. |4x3 + 36x2 + 49x + 49 |
|] | | |
|[pic|D. |4x3 + 36x2 + 63x + 49 |
|] | | |
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9. Simplify the following expression.
(7x2 - 5x + 6) + (-2x2 - 7x + 2)
|[pic|A. |5x2 - 2x + 8 |
|] | | |
|[pic|B. |9x2 - 12x + 4 |
|] | | |
|[pic|C. |5x2 - 2x - 8 |
|] | | |
|[pic|D. |5x2 - 12x + 8 |
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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?
|[pic|A. |6 |
|] | | |
|[pic|B. |-2 |
|] | | |
|[pic|C. |-6 |
|] | | |
|[pic|D. |2 |
|] | | |
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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). | |Distribute the negative. |
|2x5 + 9x4 - 17x2 + 30 - 8x5 - 13x4 - 5x2 + 5 | |Combine like terms. |
|(2x5 - 8x5) + (9x4 - 13x4) + (-17x2 - 5x2) + (30 + 5) | | |
|-6x5 - 4x4 - 22x2 + 35 | | |
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 ................
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