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Dividing Polynomials
Intro - Chapter 4.1
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Using Long DivisionExample 1:
Dividing Polynomials
DIVISOR
3 22 5 6x x x 2x
DIVIDEND
2x 4x 3
3 22x x24x 5x
3x 6 3 6x
0REMAINDER
QUOTIENT
24 8x x
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Example 2: Divide by x x3 22 6
Using Synthetic Division to Divide a Polynomial by a Divisor x – r
x 21 2 0 6 2x 2r
1
4 8 10
COEFFICIENTS OF THE
DIVIDEND
** REMEMBER PLACE
HOLDERS**
COEFFICIENTS OF QUOTIENT REMAINDER
2 8 16
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10
2x
The final answer:
21x1 4 8 102 8 16
1 2 0 62
4x 8
It Means …
x x3 22 6 2x 2 4 8x x 10
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If is divided by then
Division Algorithm:
xrxqxhxf
xf xh
f x h x q x r x
QUOTIENTDIVIDEND
REMAINDERDIVISOR
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If the remainder is 0 then, the __________ and the ______________ are factors of dividend.
If a polynomial is divided by ___________, then the remainder is __________
A polynomial function has a linear factor x – a if and only if ___________
xf
A polynomial of degree n has at most n distinct real ____________________.
Things to RememberDIVISOR
Example3: Find the remainder when is divided by x + 1
53 2479 xx
79 241 3 1 5 1 3 5 7
QUOTIENT
f cx c
0f a
ROOTS OR ZEROS
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Let be a polynomial. If r is a real number that satisfies any of the following statements, then r satisfies any of the following statements:
r is a ________ of the function f
r is an ______________ of the graph of the function f
_____ is a solution, or root of the equation ________
___________ is a factor of the polynomial f(x)
ZERO
x intercept
x r
xf
0f x
x r
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Asst. #48 Sect 4.1 pg. 248-250#1-8, 9, 18, 22, 23, 28, 39, 45, 47, 50, 51, 57, 59, 61, 64, 69