Jika suku banyak f(x) = x4 + 5x3 -2x2+Ax+B habis di bagi oleh x2-1 maka A+B adalah

Jawaban:f(x) = x^4 + 5x^3 - 2x^2 + A x + BHabis dibagi x^2 - 1 → faktor (x - 1) dan (x + 1) → f(1) = 0 dan f(-1) = 01) Substitusi x = 1:f(1) = 1 + 5 - 2 + A + B = 4 + A + B = 0→ A + B = -4 ...........(1)2) Substitusi x = -1:f(-1) = 1 - 5 - 2 - A + B = -6 - A + B = 0→ -A + B = 6 ...........(2)3) Dari (1) dan (2):A + B = -4-A + B = 6------------------ jumlahkan2B = 2B = 14) Substitusi B = 1 ke (1):A + 1 = -4A = -55) Nilai A + B:A + B = -5 + 1 = -4

Answered by dorotheaday7 | 2025-08-13

Jawab:Penjelasan dengan langkah-langkah:f(x) = x⁴ + 5x³ - 2x² + Ax + Bg(x) = x² - 1 = (x + 1) (x - 1)x + 1 = 0 ⇒ x = -1x - 1 = 0 ⇒ x = 1Karena f(x) habis dibagi g(x), maka f(-1) = f(1) = 0f(-1) = (-1)⁴ + 5(-1)³ - 2(-1)² + A(-1) + B = 01 - 5 - 2 - A + B = 0-A + B = -1 + 5 + 2-A + B = 6f(1) = (1)⁴ + 5(1)³ - 2(1)² + A(1) + B = 01 + 5 - 2 + A + B = 0A + B = -1 - 5 + 2A + B = -4-A + B = 6A + B = -4 _-2A    = 10A = 10/(-2) = - 5B = A + 6 = -5 + 6 = 1f(x) = x⁴ + 5x³ - 2x² - 5x + 1A + B = -4.

Answered by arnymatematika | 2025-08-13