What is the remainder when the polynomial 6x² + 11x - 3 is divided by 2x - 1?

Solution:

Letus divide the given polynomial 6x² + 11x - 3 by the divisor 2x - 1

Multiplying the divisor by 3x we get 6x² - 3x. Subtracting from the dividend,

Step 1: The quotient now is 3x and the remainder is 14x - 3.

Step 2: Multiplying the divisor by 7 we get 14x - 7.

Step 3: Subtracting it from 14x -3 we have the remainder 4.

2x - 1)   6x² + 11x - 3 (3x + 7
        (-) 6x² - 3x
           ----------------------
              0 + 14x - 3

               (-) 14x - 7
              --------------------
                     0 + 4

The final quotient is 3x + 7 and the remainder is 4.

What is the remainder when the polynomial 6x² + 11x - 3 is divided by 2x - 1?

Summary:

The remainder when the polynomial 6x² + 11x - 3 is divided by 2x - 1 is 4.