Q. By dividing x³ – 6x² + 2x – 4 by -3/2 x + 1, the remaining is:

Correct Answer: (A) -136/27

Explanation:

To find the remainder when dividing the polynomial f(x) = x^3 – 6x^2 + 2x – 4

by the linear divisor -3/2 x + 1, we can use the Remainder Theorem.

Steps:

1. Identify the value of x that makes the divisor zero:
-3/2 x + 1 = 0 implies x = 2/3

2. Evaluate f(2/3) to find the remainder:
f(2/3) = (2/3)^3 – 6(2/3)^2 + 2(2/3) – 4
= 8/27 – 6(4/9) + 4/3 – 4
= 8/27 – 24/9 + 4/3 – 4
= 8/27 – 72/27 + 36/27 – 108/27
= (8 – 72 + 36 – 108)/27 = -136/27

Answer: (A) -136/27