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* The terminology "mindful algebraic calculation" is also referred to as "mindful manipulation" and "manipulation using structure" It is cited in the NY Next Generation Mathematics Standards. |
Let's take a look at some questions dealing with polynomials
that may require some creative thinking.
Remember that there may be more than one way to look at these problems,
and that only one method will be shared with you as a solution.
1. Which expression is equivalent to 5a minus
the product of (a + 2) and (3a + 1) ?
| 1) -3a2 + 12a + 2 |
2) 3a2 + 2a + 2 |
3) -3a2 - 2a - 2 |
4) 3a2 + 12a + 2 |
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2. Given the expression, (a + 2b )2 - a(a + 5b) + ab, and
statement (1): a = 4
statement (2): b = 3
Which of the following sentences is true if a
simple numeric evaluation of this expression is wanted?
| 1) Neither statement ALONE is sufficient to yield a numeric answer. |
| 2) Statement 1 ALONE is sufficient to yield a numeric answer. |
3) Statement 2 ALONE is sufficient to yield a numeric answer.
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| 4) Both statements TOGETHER are NOT sufficient to yield a numeric answer. |
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3. If (x - 15)2 = 1600, which choice is one possible value for x?
| 1) x = 45 |
2) x = -25 |
3) x = -10 |
4) x= 25 |
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4. Given A = x3 + x2 - x - 2 and B = x2 + 3, what is the value of 2AB?
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The beauty of mathematics is the number of alternative ways
that can be employed to arrive at a solution.
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