Transcript 6-3 Dividing polynomials

6-3 DIVIDING
POLYNOMIALS
Synthetic division
Using synthetic division to perform long
division of polynomials
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Procedures to follow for synthetic division:
1. First, write down all the coefficients, and put the
opposite number of the divisor at the left of the vertical
line
2. Bring down the first number below the horizontal
line
3. Multiply the number at the left by the number you
brought down and put the answer above the line and
directly under the second number.
4. Add the two numbers and put the answer under
the line
5. Repeat steps 3 and 4 until the last term has been
used
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Example: Divide x2 + 5x + 6 by x + 2.
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-2
1
5
6
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write down all the coefficients, and put the zero from
x+2 = 0 (x = -2) at the left
Bring down the first number (1)
Multiply (-2) by (1) and put the answer under the (5)
Add 5 + (-2) and put the answer under the line
Multiply (-2) by (3) and put the answer under the (6)
Add (-6) to the (6) and the put the answer under the line
If the last number is “0” that means the answer is a factor of
the expression
Rewrite the answer as a polynomial beginning with one
exponent less than the highest exponent of the original
polynomial (x+3)
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So the factors of x2 + 5x + 6 are (x+2) and (x+3)
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h/w: p. 324: 13, 14, 16, 17
Divide (x3 + 2x2 - 5x – 6) by (x+1)