Question

When a polynomial f(x) is divided by (x – 3) and (x + 6), the respective remainders are 7 and 22. What is the remainder when f(x) is divided by (x – 3) (x + 6) ? 

(a) \(\frac{-5}{3}x+12\)

(b) \(-\frac{7}{3}x+14\)

(c) \(-\frac{5}{3}x+16\)

(d) \(-\frac{7}{3}x+12\)

Answer 1

(a) \(\frac{-5}{3}x+12\)

The function f(x) is not known. Here, 

a = 3, b = – 6 

A = 7, B = 22                  [Refer to Key Fact 8] 

∴ Required remainder = \(\frac{A-B}{a-b}x+\frac{Ba-Ab}{a-b}\)

= \(\frac{7-22}{3-(-6)}x+\frac{22\times3-7\times(-6)}{3-(-6)}\) = \(\frac{-5}{3}x+12.\)