Diketahui suku banyak f(x) = 2x⁴ + ax³ - 6x² + bx - 3. Jika f(1) = -3 dan f(-2) = 3, nilai a - b = .... A. 6 B. 4 C. 2 D. -4 E. -6

<p>Jawaban: E</p><p>&nbsp;</p><p>Ingat bahwa!</p><p>Sisa pembagian suku banyak P(x) oleh (x+k) adalah &nbsp;P(-k)&nbsp;</p><p>&nbsp;</p><p>f(x) = 2x⁴ + ax³ - 6x² + bx - 3&nbsp;</p><p>f(1) = 2(1)⁴ + a(1)³ - 6(1)² + b(1) - 3&nbsp;</p><p>-3 = 2+a-6+b-3</p><p>a+b = 4 ...pers 1</p><p>f(-2) = 2(-2)⁴ + a(-2)³ - 6(-2)² + b(-2) - 3&nbsp;</p><p>3 = 32-8a-24-2b-3</p><p>8a+2b = 2 ...pers 2</p><p>&nbsp;</p><p>Eliminasi pers 1 dan 2</p><p>a+b = 4 &nbsp; &nbsp;|×2|2a+2b=8</p><p>8a+2b =2|×1|8a+2b=2</p><p>___________________ -</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;-6a = 6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;a = -1</p><p>(-1)+b = 4</p><p>b = 4+1</p><p>b = 5</p><p>&nbsp;a-b = -1-5 = -6</p><p>&nbsp;</p><p>jadi, jawaban yang tepat adalah E</p>