4 Polynomials
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I , , . I , , ( ).
. , . F ,
= 2 + 2. 0 2, (0) = 2. I 4 18, (4) = 18, 2
6, ( 2) = 6. A .
, , . .
, , .
= 2 = 2 = 6, ( ) ≥ 0 > 0. F
, ≥ 0.
, ; , ( , ) . E , ( ) = ;
,
. I ( 1), .
= = + , , = = 0, (0,
A 1 .
. = + 11 + 1
1 + 0 , .
( , ) . .
A ( ) = 22 + 1 + 0 ,
( ), 22 + 1 + 0 = 0, .
. 2, 2 , . I 2 ; .
( ), .
, ( )
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: , I , . I
, . ≠ .
• G : ...• ∈ * • , , ( .
).• , , ∈
E : 2 3, 4 2 , 7 2 4 3.
• D : .
E : 1) = 3 2 1+2+1 = 4
2) = 2 .
3) = 0 ∞ ( )
• L :
E : 2 3
5 3
: 2 3 + 5 3 = 7 3
: 23 5 3 = 3 3
• : .
E : I 1= 2 3 4 2 = 3 2 3
1 × 2 = 2 3 4 × 3 2 3 = ( ) 6 3 4 × 2 3
1 × 2 = 6 5 7 .
• D : , .E : 3 2 + 3 2 2
• : A : ,
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• D = .E : F = 3 2+ 3 2 2
(3 2) = 2+1 = 3
(3 2) = 3+2 = 5
(2 ) = 2+1+1 = 4
. ,
•
•
• . F • G : ( ) = + 1
1 + 11 + 0
• , 1, 1, 0 • F • E : ( ) = 2 3 + 2 1 , (2) = 2 × (2) 3 + 2 × 2 1 = 19•
• :• E : ( ) = 34 + 5 2 + 2 2 + 3 + 5 4
34 5 4, 5 2 2 2. : ( ) =8 4 + 7 2 + 3
• .
•
E : 1 ( ) = 2 + + , ,
2 ( ) = 3 2 2 + 5
1 2 ( 1 ≡ 2) = 3, = 2, = 5
• A
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E : ( ) = 3 + 2 + +
( ) ≡ 0 = 0, = 0, = 0, = 0
• .
E : 1 ( ) = 3 3 +7 2 + 4 3
2 ( ) = 4 4 2 2 + 3 + 4
1 ( ) + 2 ( ) = (3 3 +7 2 + 4 3) + ( 4 4 2 2 + 3 + 4)
E 2 1 ( ) + 2 ( ) = 3 3 +7 2 + 4 3 4 4 2 2 + 3 + 4
A : 1 ( ) + 2 ( ) = 4 4 + 3 3+ 5 2 + 7 +1
• A ( )
E : 1 ( ) = 3 3 +7 2 + 4 3
2 ( ) = 4 4 2 2 + 3 + 4
1 ( ) 2 ( ) = (3 3 +7 2 + 4 3) ( 4 4 2 2 + 3 + 4)
2 :
3 3 +7 2 + 4 3 + 4 4 + 2 2 3 4)
A :
1 ( ) 2 ( )= 4 4 + 3 3 +9 2 + 7
•
.•
.E : 1( ) = 2 5 3
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2( ) = 2 2 3
E = 1 × 2
1 ( ) × 2 ( ) = (2 5 3) × (2 2 3) = 2 5 × (2 2 3) 3 × (2 2 3) = 4 7 6 5 6 2 + 9.
5 +2 = 7.
• B
.• • :
E : 1 ( ) = 3 4 3 2 + 1 2 ( ) = 2 + 3
1: :
3 4 3 2 + 1 2 + 3
2: 1 ( . : 3 4) 2 ( . : 2)
2
4
xx3
= 3 2. 2
3 4 3 2 + 1 2 + 3
3 2
3: 32 2
3 4 + 3 3 9 2
1
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3 4 3 2 + 1 2 + 3
3 4 + 3 3 9 2 3 2
4 : 34 + 3 3 9 2 1 A( ) = 33 + 6 2 + 1
:
3 4 3 2 + 1 2 + 3
3 4 + 3 3 9 2
3 3 + 6 2 + 1 3 2
5: A 2
2
3
xx3−
= 3
32 :
3 4 3 2 + 1 2 + 3
3 4 + 3 3 9 2
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3 3 + 6 2 + 1 3 2 3
6 : 3 2
3 3 3 2 + 9
A :
3 4 3 2 + 1 2 + 3
3 4 + 3 3 9 2
3 3 + 6 2 + 1 3 2 3
3 3 3 2 + 9
7: 33 3 2 + 9 A
A2( ) = 9 2 9 + 1
:
3 4 3 2 + 1 2 + 3
3 4 + 3 3 9 2
3 3 + 6 2 + 1 3 2 3
3 3 3 2 + 9
9 2 9 + 1
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8: A2 2
2
2
x
x9= 9
32 3 :
3 4 3 2 + 1 2 + 3
34
+ 33
92
3 3 + 6 2 + 1 3 2 3 + 9
3 3 3 2 + 9
9 2 9 + 1
9: 9 2
92
+ 9 27
A2 :
3 4 3 2 + 1 2 + 3
3 4 + 3 3 9 2
33
+ 62
+ 1 32
3 + 9
3 3 3 2 + 9
9 2 9 + 1
9 2 + 9 27
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10: 92 + 9 27 A2
A3( ) = 28 18
:
3 4 3 2 + 1 2 + 3
3 4 + 3 3 9 2
3 3 + 6 2 + 1 3 2 3 + 9
3 3 3 2 + 9
9 2 9 + 1
9 2 + 9 27
28 18
• ( ) = 18 +28 2 .
•
1
• 2 • 2 . .• .• H , 1 1 = 2 × +
I ( ) = 0 2 1. 1 2 1 2
• 1: A .• 2: D .
• 3: .
• 4: C . I 7. E , 5.
• 5: 3
• 6: G 3• 7: E
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