Question

What should be subtracted from 27x³ – 9x² – 6x – 5 to make it exactly divisible by (3x – 1)

(a) –5 

(b) –7 

(c) 5 

(d) 7

Answer 1

(b) -7

To make f(x) = 27x³ – 9x² – 6x – 5 exactly divisible by (3x – 1), the remainder obtained on division should be subtracted.

Remainder = \(f\big(+\frac{1}{3}\big)\) = 27 x \(\big(\frac{1}{3}\big)^3\) - 9 x \(\big(\frac{1}{3}\big)^2\) - 6 x \(\frac{1}{3}\) - 5 

\(\big(∵3x-1 =0 ⇒x=\frac{1}{3}\big)\)

= 1 – 1 – 2 – 5 = – 7.