Tentukan nilai A, B, dan C jika diketahui: a. (2x + 1)(3x - 7) = Ax2 + Bx - 7 b. 3x² - 10x - 8 = (Ax + 2)(x - B)

Tentukan nilai A, B, dan C jika diketahui:

a. (2x + 1)(3x - 7) = Ax² + Bx - 7

b. 3x² - 10x - 8 = (Ax + 2)(x - B)

c. -4x + 13 = A(2x - 5) + B(3x - 6)

d. 7x² - 8x - 10 = (Ax + B)(x - 2) + (B + C)x

e. 11x² + 4x + 12 = A(x² + 4) + (Bx + C)(2x + 1)

f. A(x - 2)(x + 1) + B(x - 1)(x + 3) + C(x + 2)(x – 3) = 9x + 17

Jawab:

a. (2x + 1)(3x – 7) = Ax² + Bx – 7

    6x² – 11x – 7 = Ax² + Bx – 7

    A = 6 dan B = -11

b. 3x² – 10x – 8 = (Ax + 2)(x - B)

    (3x + 2)(x – 4) = (Ax + 2)(x - B)

    A = 3 dan B = 4

c. -4x + 13 = A(2x - 5) + B(3x - 6)

    -4x + 13 = 2Ax – 5A + 3Bx – 6B

    -4x + 13 = (2A + 3B)x + (-5A – 6B)

    2A + 3B = -4 (dikali 2)

    4A + 6B = -8

    -5A – 6B = 13 +

    -A = 5 → A = -5 dan B = 2

d. 7x² – 8x – 10 = (Ax + B)(x - 2) + (B + C)x

    7x² – 8x – 10 = Ax² + (-2A + B)x – 2B + (B + C)x

    7x² – 8x – 10 = Ax² + (-2A + 2B + C)x – 2B

    A = 7

    -2B = -10 ⇔ B = 5

    -2A + 2B + C

    ⇔ -2(7) + 2(5) + C = -8

    ⇔ -14 + 10 + C = -8

    ⇔ C = = -8 + 14 – 10 = -4

e. 11x² + 4x + 12 = A(x² + 4) + (Bx + C)(2x + 1)

    11x² + 4x + 12 = Ax² + 4A + 2Bx² + Bx + 2Cx + C

    11x² + 4x + 12 = (A + 2B)x² + (B + 2C)x + (4A + C)

    A + 2B = 11

    B + 2C = 4

    4A + C = 12

    B + 2C = 4

    8A + 2C = 24 _

    8A – B = 20

    A + 2B = 11

    16A – 2B = 40

    17A = 51

        A = 3

    A + 2B = 11

    3 + 2B = 11

    2B = 8

    B = 4

    B + 2C = 4

    4 + 2C = 4

    C = 0

     

f. A(x - 2)(x + 1) + B(x - 1)(x + 3) + C(x + 2)(x – 3) = 9x + 17

   A(x² – x – 2) + B(x² + 2x – 3) + C(x² – x – 6) = 9x + 17

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Ingat Cita-Cita, Orang Tua, dan Keluarga

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