# Synthetic Division

```By: Group Awesome
Arianna, Brittany, Dana, Julie and Raymond
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Lesson Plan
Objective: To learn how to divide polynomials using Synthetic Division
Method:
 Use a powerpoint
 Demonstrate, using a model
 Provide practice problems
Procedure: First, we will provide a sample problem to demonstrate the
process of synthetic division for the class. After fully explaining the process
of synthetic division, we will distribute a handout that contains several
practice problems for the class to complete. At the end of the lesson, we will
go over the sheet.
Materials: A powerpoint with the example problem, copies of a worksheet
with the practice problems
Evaluation: We will be able to tell if we have effectively taught the lesson if
the students are able to correctly do the practice problems that we have
given them, which will demonstrate that they both understand the concept of
the lesson and how to put the strategy into effect.
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Synthetic division is a shorthand, or shortcut,
method of polynomial division in the special
case of dividing by a linear factor and
it only works in this case.
Synthetic division is generally used, however,
not for dividing out factors but for finding
zeroes of polynomials.
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Create an upside down division symbol, with the
zero on the outside, and the coefficients of the
polynomial on the inside, including the powers not
included, such as x2, and x. (x3+0x2+0x-1). The
first number inside gets carried down to the
bottom.
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Multiply the zero (number outside) by the
carried down number. The result goes onto
the second column. Add the numbers in the
second column. Continue doing this until you
reach the end
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The last number is the remainder of the
division problem, and if the remainder is
zero, then x=1 is a zero of x3-1.
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For x – 4 to be a factor, you must have x =
4 as a zero. Using this information, I'll do the
synthetic division with x = 4 as the test zero
on the left:
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Yes, x – 4 is a factor of –2x5 + 6x4 + 10x3 –
6x 2 – 9x + 4
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