Hasil bagi suku banyak P(x) = x⁵ - 3x⁴ + 2x³ + 4x - 9 oleh x² - 5x + 6 adalah . . . . A. x³ - 2x² - 6x - 13 B. x³ - 2x² + 6x + 13 C. x³ + 2x² - 6x + 13 D. x³ + 2x² + 6x - 13 E. x³ + 2x² + 6x + 13

<p>Jawaban: E</p><p>&nbsp;</p><p>Asumsikan soal:</p><p>Hasil bagi suku banyak P(x) = x⁵ - 3x⁴ + 2x³ + 4x - 9 oleh x² - 5x + 6 adalah . . . .<br>A. x³ - 2x² - 6x - 18<br>B. x³ - 2x² + 6x + 18<br>C. x³ + 2x² - 6x + 18<br>D. x³ + 2x² + 6x - 18<br>E. x³ + 2x² + 6x + 18</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; &nbsp; &nbsp;x³+ 2x² + 6x + 18 → hasil bagi</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;_________________</p><p>x² - 5x + 6 / x⁵ - 3x⁴ + 2x³ + 4x - 9</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;x⁵ - 5x⁴+ 6x³</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; 2x⁴- 4x³+ 4x - 9</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2x⁴- 10x³+ 12x²</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;6x^3&nbsp;-12x² + 4x - 9</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; &nbsp; &nbsp;&nbsp;}6x³ - 30x² + 36x</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; &nbsp;18x² - 32x - 9</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; &nbsp;18x² - 90x + 108</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; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 58x - 117 → sisa</p><p>&nbsp;</p><p>Jadi, hasil bagi suku banyak P(x) = x⁵ - 3x⁴ + 2x³ + 4x - 9 oleh x² - 5x + 6 adalah x³+ 2x² + 6x + 18.</p><p>Oleh karena itu, jawaban yang benar adalah E.</p>