Diketahui g(x) = x³ + px² - 2x + q dan h(x) = x² - 2x- 8 merupakan faktor dari g(x). Dengan demikian nilai p = …. A. -5 B. -6 C. -7 D. -8 E. -9

<p>Jawab: A</p><p>Pembahasan:</p><p>Teorema Faktor:</p><p>Misal P(x) adalah suku banyak. Jika (x-k) adalah faktor dari P(x) maka P(k) = 0.</p><p>Perhatikan bahwa &nbsp;h(x) = x² - 2x- 8</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;= (x-4)(x+2)</p><p>Sehingga, g(4) = g(-2) = 0.</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; g(4) = 0</p><p>4³ + p(4²) - 2(4) + q = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;64+16p-8+q = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;16p+q+56 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;16p+q = -56 &nbsp;...1)</p><p>Dan,</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;g(-2) = 0</p><p>(-2)³ + p((-2)²) - 2(-2) + q = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;-8+4p+4+q = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 4p+q-4 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 4p+q = 4 ...2)</p><p>Dari persamaan 1) dan 2), menglemininasi q untuk menentukan nilai p.</p><p>16p+q = -56</p><p>&nbsp; 4p+q = 4 &nbsp; &nbsp; &nbsp; -</p><p>----------------------</p><p>&nbsp; &nbsp; &nbsp;12p = -60</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; p = -5</p><p>Sehingga, nilai p adalah -5.</p><p>&nbsp;</p><p><strong><u>Jadi, jawaban yang benar adalah A.</u></strong></p>