Matematika

Pertanyaan

Jika suku banyak f(x) dibagi x2 - x sisa pembagiannya 3x + 4 dan jika dibagi x2 + x - 6 sisa pembagiannya 2x + 5. Sisa pembagian jika f(x) dibagi x2 + 2x - 3...
a. 2x - 5
b. 2x + 5
c. 3x - 1
d. 5x + 2
e. 5x - 2

1 Jawaban

  • f(x) : (x^2 - x) bersisa (3x + 4)
    x^2 - x = x(x - 1) => x = 0 atau x = 1
    f(0) = 3(0) + 4 = 4
    f(1) = 3(1) + 4 = 7

    f(x) : (x^2 + x - 6) bersisa (2x + 5)
    x^2 + x - 6 = (x + 3)(x - 2) => x = -3 atau x = 2
    f(-3) = 2(-3) + 5 = -1
    f(2) = 2(2) + 5 = 9

    f(x) : x^2 + 2x - 3 bersisa (ax + b)
    x^2 + 2x - 3 = (x + 3)(x - 1) => x = -3 atau x = 1
    f(-3) = a(-3) + b => -3a + b = -1
    f(1) = a(1) + b ======> a + b = 7
    ------------------------------------------- --
    ....................................... -4a = -8 => a = 2
    a + b = 7 => 2 + b = 7 => b = 5
    Sisa = ax + b = 2x + 5

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