中四數學問題,請教

Let x³ + x² - 3x - 4 = p(x) f(x) - x + 4 , where f(x) is a polynomial of degree > 1 and not more than 3 , then x³ + x² - 2x - 8 = p(x) f(x).Note that p(2) f(2) = (2)³ + (2)² - 2(2) - 8 = 0 ,
by remainder theorem, x - 2 is a factor of x³ + x² - 2x - 8.
x³ + x² - 2x - 8
= x³ - 8 + x(x - 2)
= (x - 2)(x² + 2x + 4) + x(x - 2)
= (x - 2)(x² + 3x + 4)∴ p(x) = x - 2 , f(x) = x² + 3x + 4 , the answer is D.

由於 remainder 是 polynomial of degree 1
你可以考慮 divisor 是 polynomial of degree larger than 1
a. 和 b. 可以被否決。

再考慮 (dividend - remainder) 要可以被 divisor f(x) 整除，你就可以知道是 c. 和 d. 之中的哪一個。