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Re: Reply to a Post of 2/06/09 Why Robert Atkin method of factoring trinomials works
Posted:
Apr 21, 2009 10:22 AM
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If I were a secondary school teacher, I would have to teach factoring quadratics because my students would need to do it on standardized tests. Do community college teachers have similar restrictions? If not, why teach it with so much emphasis on being able to do it quickly by hand? Factoring itself is important, but factoring quadratics can be done via completing the square just as one might to derive the quadratic formula. Students put the quadratic formula on their calculators. It wouldn't be much different to put on a small program to factor. In order to build conceptual understanding, I would prefer a course that reinforced these aspects including teaching the students to do the programming themselves,either on their calculator or on a spreadsheet.
Fred Siegeltuch
--- On Tue, 4/21/09, Annette Hawkins <hawkins@waynecc.edu> wrote:
From: Annette Hawkins <hawkins@waynecc.edu>
Subject: Re: Reply to a Post of 2/06/09 Why Robert Atkin method of factoring trinomials works
To: mathedcc@mathforum.org, jritchey5072@yahoo.com
Date: Tuesday, April 21, 2009, 7:57 AM
Please don't use this method because:
1. When the students enter College Algebra, they can't keep up with
the instructor when he/she has to factor a problem. These students are
left in the dust in a College Algebra class.
2. They have no clue how to factor trig equations and exponential
equations.
3. The idea is to think about where the terms come from in the
trinomial and undo the process. Some thinking is required.
Just my two cents.
Annette D. Hawkins, Ed. D.
Math Department Head
Wayne Community College
3000 Wayne Memorial Drive
Goldsboro, NC 27534
919-735-5151 x 709
hawkins@waynecc.edu
>>> <jritchey5072@yahoo.com> 4/20/2009 4:03 PM >>>
I have the same text book (Sullivan Algebra Trigonometry, 4 ed.) and
came across the same method for factoring trinomials. I LOVE IT! I am
the tutor at a community college, and, after discussing the method with
an instructor and understanding its mathematical process, I regularly
show it to my students.
The reason this method works is due to the factoring out of the common
factors.
Given the trinomial: 6x^2 - x - 12
Multiply coefficient a with constant c 6(-12) = -72
Factors of -72 whose difference (or sum) is 1 are 8 and -9
The coefficient of the leading term and the square root of the variable
are then written as the first term of each factor:
(6x )(6x )
Then the 8 and -9 are inserted into their positions as the second:
(6x + 8)(6x - 9)
What is NOT shown in the text book (page 47), is that the factors must
be understood to be written over a common factor of the EXTRA number
used in the second factor, in this case 6.
(6x + 8)(6x - 9)
----------------------
6
When the GCF's are removed from each factor, the real factors are
obtained, and the common factors are cancelled by the common
denominator.
2(3x + 4)(2x - 3)3
----------------------
6
(3x + 4)(2x - 3)
NOTE: Just as with any other method of factoring trinonials, make sure
ALL GCF's are removed as the first step.
E-?Mail correspondence to and from this sender may be subject to the
North Carolina public records law and may be disclosed to third parties.
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