Sisa pembagian suku banyak P(x) = x⁵ - 1 oleh x² - x - 2 adalah .... A. 11x + 11 B. 11x + 9 C. 11x - 9 D. -11x + 11 E. -11x +9

<p>Jawaban: B</p><p>&nbsp;</p><p>Konsep:</p><p>Cara pembagian bersusun pada suku banyak:</p><p>1. Bagi Suku banyak dengan variabel tertinggi ke pembagi variabel tertinggi</p><p>2. Kalikan hasilnya dengan pembagi</p><p>3. Kurangi Suku banyak dengan hasil kali pada langkah 2</p><p>4. Bagi kembali sisa Suku banyak variabel tertinggi dengan pembagi variabel tertinggi</p><p>5. Langkah berlanjut sampai sisa Suku banyak tidak dapat dibagi lagi oleh pembagi</p><p>&nbsp;</p><p>Pembahasan:</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x³+ x² + 3x + 5 → hasil bagi</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;___________</p><p>x² - x - 2 / x⁵ - 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x⁵ - x⁴- 2x³</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;____________________-</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x⁴+ 2x³- 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x⁴- x³- 2x²</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;____________________-</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3x^3&nbsp;+2x² - 1</p><p>^{&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;}3x³ - 3x² - 6x</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;____________________-</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5x² + 6x - 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5x² - 5x - 10</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;____________________-</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 11x + 9 → sisa</p><p>&nbsp;</p><p>Jadi, sisa pembagian suku banyak P(x) = x⁵ - 1 oleh x² - x - 2 adalah &nbsp;11x + 9.</p><p>Oleh karena itu, jawaban yang benar adalah B.</p>