jika (x-1)^2 membagi ax^4+bx^3+1 tentukan ab

(x - 1)^2 = (x - 1)(x - 1) => x = 1
Membagi (ax^4 + bx^3 + 1)
= ax^4 + bx^3 + 0x^2 + 0x + 1
1 | a ....... b .............. 0 ............ 0 .............. 1
.. | ......... a ............ a + b ...... a + b ....... a + b
------------------------------------------------------------ +
1 | a ...... a + b ...... a + b ........ a + b ... | ... a + b + 1 = 0 => a + b = -1
.. | ......... a ............ 2a + b ...... 3a + 2b
----------------------------------------------- +
..... a .... 2a + b ... 3a + 2b ..|.. 4a + 3b = 0

Eliminasi
a + b = -1 |.4| 4a + 4b = -4
....................... 4a + 3b = 0
------------------------------------ --
................................... b = -4

a + b = -1 => a + (-4) = -1 => a = 3

ab = 3(-4) = -12

(x - 1)^2 = (x - 1)(x - 1) = x^2 - 2x + 2

x^2 - 2x + 2 / ax^4 + bx^3 + 1 = 0
1 / -a -b= 0
-a - b = 1
a + b = -1

(x-1)^2 = (x-1)(x-1)

ax^4 + bx^3 + 1 = 0
(a + bx) (x/2 - 1) ( x - 1) = 0
(x - 1)(x -1) / (a + bx)(x^2 - 1)(x - 1) = 0
(x - 1) / (a + bx )( x^2 - 1) = 0
2(x-1) / 2(a + bx)(x^2 - 1) = 0
2 / (8a + 6b) + 1= 0
1 / 4a + 3b + 1= 0
1 = 4a + 3b + 1
0 = 4a + 3b

4a + 3b = 0 | kali 1
a + b = -1 | kali 4
_________
4a + 3b = 0
4a + 4b = -4 ( - )
__________
-b = 4
b = -4

a + b = -1
a + (-4) = -1
a - 4 = -1
a = -1 + 4
a= 3

ab =
a(b) =
3(-4) =
-12

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