Diketahui 2x² + 3x - 2 merupakan faktor dari suku banyak P(x) = 2px⁴ - x³ - 6x² + (q + 3)x - 2. Nilai dari p³ + q³ = .... A. 9 B. 65 C. 126 D. 133 E 152

<p>Jawaban: B</p><p>&nbsp;</p><p>Ingat bahwa!</p><p>Teorema faktor</p><p>Jika (x+k) adalah faktor dari suku banyak f(x) maka f(-k) = 0&nbsp;</p><p>&nbsp;</p><p>2x² + 3x - 2 = (2x-1)(x+2) adalah faktor dari P(x) = 2px⁴ - x³ - 6x² + (q + 3)x - 2 maka&nbsp;</p><p>P(½) = 2p(½)⁴ - (½)³ - 6(½)² + (q + 3)(½) - 2</p><p>0 = p/8 - 1/8 - 3/2 +q/2 +3/2 -2</p><p>p/8 + q/2 = 17/8&nbsp;</p><p>p/8 + 4q/8 = 17/8 (kedua ruas dikalikan 8)</p><p>p + 4q = 17 ...pers 1</p><p>&nbsp;</p><p>P(-2) = &nbsp;2p(-2)⁴ - (-2)³ - 6(-2)² + (q + 3)(-2) - 2</p><p>0 = 32p +8-24-2q-6-2</p><p>32p-2q = 24 ...pers 2</p><p>&nbsp;</p><p>Eliminasi pers 1 dan 2</p><p>p+4q = 17 &nbsp; &nbsp; |×1|p+4q = 17</p><p>32p-2q =24|×2|64p-4q=48</p><p>________________________ +</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 65p = 65</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; p = 1</p><p>1 + 4q = 17</p><p>4q = 17-1</p><p>4q = 16</p><p>q = 4</p><p>sehingga&nbsp;</p><p>p³ + q³ = 1³ + 4³&nbsp;</p><p>p³ + q³ = 1 + 64</p><p>p³ + q³ = 65</p><p>&nbsp;</p><p>Jadi, jawaban yang tepat adalah B.</p>