6­3 Day 2 Dividing Polynomials January 21, 2010
6.3 Dividing Polynomials
Day 2
Objective: Divide polynomials using synthetic division.
Jan 8­9:41 AM
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6­3 Day 2 Dividing Polynomials January 21, 2010
Check Skills You'll Need
Simplify and write in standard form.
1. 5x - 2x2 + 9 + 4x3
2. 10 + 5x3 - 9x2 - 8x3
3. 3x + x2 - x + 7 - 2x2
4. -4x4 - 7x2 + x3 + x4
Jan 8­9:46 AM
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6­3 Day 2 Dividing Polynomials January 21, 2010
Review:
Use long division to divide 2x2 - 19x + 24 by x - 8.
Is x - 8 a factor of 2x2 - 19x + 24?
Jan 8­9:46 AM
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6­3 Day 2 Dividing Polynomials January 21, 2010
Synthetic Division
If you are dividing a polynomial by a linear
polynomial you can use a shortcut called
synthetic division.
Yea we love shortcuts!!
Jan 8­10:31 AM
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6­3 Day 2 Dividing Polynomials January 21, 2010
Example #1: Divide 2x3 - x2 + 3 by x - 3.
dividend
divisor
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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6­3 Day 2 Dividing Polynomials January 21, 2010
Example #1: Divide 2x3 - x2 + 3 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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6­3 Day 2 Dividing Polynomials January 21, 2010
Example #1: Divide 2x3 - x2 + 3 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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6­3 Day 2 Dividing Polynomials January 21, 2010
Example #1: Divide 2x3 - x2 + 3 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
5x 3 15x 3 48
Row 2
Row 3
Quotient = 2x2 + 5x + 15
Remainder = 48
***The Quotient is a factor of the Dividend if the Remainder is ZERO!!
Nov 18­2:14 PM
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6­3 Day 2 Dividing Polynomials January 21, 2010
Example #2:
Use synthetic division to divide 3x3 - 4x2 + 2x - 1 by x + 1.
Is x + 1 a factor of 3x3 - 4x2 + 2x - 1?
Jan 8­9:49 AM
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6­3 Day 2 Dividing Polynomials January 21, 2010
Example #3:
Use synthetic division to divide x3 + 4x2 + x - 6 by x + 1.
Is x + 1 a factor of x3 + 4x2 + x - 6?
Jan 8­9:49 AM
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6­3 Day 2 Dividing Polynomials January 21, 2010
Example #4:
Use synthetic division to divide x3 - 2x2 - 5x + 6 by x + 2.
Is x + 2 a factor of x3 - 2x2 - 5x + 6?
Jan 8­9:49 AM
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6­3 Day 2 Dividing Polynomials January 21, 2010
Homework:
page 324
(13 - 22, 48 - 51)
Homework is
Jan 8­2:01 PM
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