Question

Bantu jawab soal nomor 1, 2, dan 3 dengan cara....

Answer 1

1) f(x) = 3x^3 - 2x + 5 : (x - 2) => x = 2
2 | 3 ... 0 ... -2 ... 5
... | ...... 6 .... 12 ... 20
---------------------------- +
..... 3 ... 6 .... 10 | 25
Hasil bagi = 3x^2 + 6x + 10
Sisa = 25

2) f(x) = 2x^3 + x^2 + 4x - 4 : (2x - 3) => x = 3/2
3/2 | 2 ... 1 ... 4 ... -4
....... | ..... 3 ... 6 .... 15
---------------------------- +
........ 2 .. 4 ... 10 | 11
Hasil bagi = 2x^2 + 4x + 10
Sisa = 11

3) f(x) = 2x^3 + 5x^2 + ax + b
1) f(x) : (x + 1) bersisa 1 => f(-1) = 1
f(-1) = 2(-1)^3 + 5(-1)^2 + a(-1) + b = 1
=> -2 + 5 - a + b = 1
=> -a + b = -2

2) f(x) : (x - 2) bersisa 43 => f(2)= 43
f(2) = 2(2)^3 + 5(2)^2 + a(2) + b = 43
=> 16 + 20 + 2a + b = 43
=> 2a + b = 7

Eliminasi
-a + b = -2
2a + b = 7
------------------ -
-3a = -9 => a = 3

-3 + b = -2 => b = 1

2a + 3b = 2(3) + 3(1) = 9