A.4 Synthetic Division 2010
September 10, 2010
Synthetic Division
Objective - Use synthetic division to find the quotient of two polynomials
Nov 18­1:50 PM
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A.4 Synthetic Division 2010
September 10, 2010
Synthetic Division:
Used to find the quotient and remainder when a
polynomial of degree 1 or higher is divided by x - c.
YAY...this is a short cut for long division!!
Nov 18­1:52 PM
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A.4 Synthetic Division 2010
September 10, 2010
Example: 2x3 - x2 + 3 divided by x - 3
Step 1: Write the dividend in descending powers of x. Then copy the
coefficients, remembering to insert a zero for any missing powers of x.
2
-1
0
3 Row 1
Step 2: Insert the usual division symbol. In synthetic division the divisor
is of the form x - c, and c is the number placed to the left of the division
symbol. Here we insert 3.
3 2
-1
0
3 Row 1
Nov 18­2:14 PM
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A.4 Synthetic Division 2010
September 10, 2010
Example: 2x3 - x2 + 3 divided by x - 3
Step 3: Bring the 2 down two rows, and enter it in row 3.
3 2
-1
0
3 Row 1
Row 2
2
Row 3
Step 4: Multiply the latest entry in row 3 by the divisor (3 in this case),
and place the result in row 2, one column over to the right.
3 2
2
-1
6
x3
0
3 Row 1
Row 2
Row 3
Nov 18­2:14 PM
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A.4 Synthetic Division 2010
September 10, 2010
Example: 2x3 - x2 + 3 divided by x - 3
Step 5: Add the entry in row 2 to the entry above it in row 1, and enter
the sum in row 3.
3 2
2
x3
-1
6
5
0
3 Row 1
Row 2
Row 3
Step 6: Repeat Steps 4 and 5 until no more entries are available in row 1.
3 2
2x 3
-1 0 3 Row 1
6 15 45 Row 2
3
3
5x 15x 48 Row 3
Nov 18­2:14 PM
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A.4 Synthetic Division 2010
September 10, 2010
Example: 2x3 - x2 + 3 divided by x - 3
Step 7: The final entry in row 3 is the remainder, the other entries are
the coefficients in descending order of a polynomial whose degree is one
less than that of the dividend.
3 2
2x 3
-1 0 3 Row 1
6 15 45 Row 2
3
3
5x 15x 48 Row 3
Quotient = 2x2 + 5x + 15
Remainder = 48
Nov 18­2:14 PM
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A.4 Synthetic Division 2010
September 10, 2010
Homework: page 983 (21 - 32)
I love...
math Nov 18­1:52 PM
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