若a,b為整數,且x²-x-1為ax³+bx²+1的因式,則b的值為何?

當 ax³ + bx² + 1 除以 x² - x - 1 時，商數必為 ax - 1

考慮 ax³ + bx² + 1 = (x² - x - 1) (ax - 1) = ax³ - (a + 1)x² - (a - 1)x + 1
∵ x 的係數 = 0
- (a - 1) = 0
a = 1

∴ b = - (a + 1) = - (1 + 1) = -2