Tentukan a, jika 2x3 - 5x² - ax + 7 habis dibagi 2x + 1.

<p><strong>Untuk menentukan nilai a sehingga 2x^3 - 5x^2 - ax + 7 habis dibagi oleh 2x + 1, kita dapat menggunakan pembagian polinomial (polynomial long division). Berikut adalah langkah-langkahnya:</strong></p><p><strong>Pertama-tama, kita harus membagi 2x ke dalam 2x^3 yang akan menghasilkan x^2:</strong></p><p><strong>scss</strong></p><p><strong>&nbsp; &nbsp; &nbsp; &nbsp;x² &nbsp; &nbsp;___________ 2x + 1 | 2x³ - 5x² - ax + 7 &nbsp; &nbsp; &nbsp; -(2x³ + x²) &nbsp; &nbsp; &nbsp; ___________ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - 4x² - ax + 7</strong></p><p><strong>Selanjutnya, kita membawa turun -4x^2 dan membagi 2x ke dalam -4x^2, yang menghasilkan -2x:</strong></p><p><strong>scss</strong></p><p><strong>&nbsp; &nbsp; &nbsp; &nbsp;x² - 2x &nbsp; &nbsp;___________ 2x + 1 | 2x³ - 5x² - ax + 7 &nbsp; &nbsp; &nbsp; -(2x³ + x²) &nbsp; &nbsp; &nbsp; ___________ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - 4x² - ax + 7 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - (-4x² - 2x) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ___________ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - ax + 7</strong></p><p><strong>Selanjutnya, kita membawa turun -ax dan membagi 2x ke dalam -ax, yang menghasilkan -a/2:</strong></p><p><strong>scss</strong></p><p><strong>&nbsp; &nbsp; &nbsp; &nbsp;x² - 2x - (a/2) &nbsp; &nbsp;___________ 2x + 1 | 2x³ - 5x² - ax + 7 &nbsp; &nbsp; &nbsp; -(2x³ + x²) &nbsp; &nbsp; &nbsp; ___________ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - 4x² - ax + 7 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - (-4x² - 2x) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ___________ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - ax + 7 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - (-ax - a/2) &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;(a/2) + 7</strong></p><p><strong>Sekarang, kita ingin agar sisa dari pembagian ini menjadi nol, sehingga kita memiliki persamaan:</strong></p><p><strong>css</strong></p><p><strong>(a/2) + 7 = 0</strong></p><p><strong>Kemudian, kita dapat menyelesaikan persamaan ini untuk mencari nilai a:</strong></p><p><strong>css</strong></p><p><strong>(a/2) + 7 = 0 (a/2) = -7 a = -14</strong></p><p><strong>Jadi, nilai a yang membuat 2x^3 - 5x^2 - ax + 7 habis dibagi oleh 2x + 1 adalah a = -14</strong></p>