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Mindful Algebraic Calculations*
Involving Factoring
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Topical Outline | Algebra 1 Outline | MathBits' Teacher Resources

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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.

mindpuzzle

Let's take a look at some questions dealing with factoring
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.   If p and q are constants, and x2 + px + 6
is equivalent to (x + 2)(x + q),
what is the value of p ?

 

2.   What are the zeros of the trinomial
3x3 - 21x2 + 30x ?

 

3.    If   and x ≠ -4,
what is the value of x?

 

4.    Factor completely:    x2 (x - 2) - (9x - 20)(x - 2)

 

The beauty of mathematics is the number of alternative ways
that can be employed to arrive at a solution.


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