Show how you will find the remainder when 2x^2 + 5x – 3 is divided x + 3 by using synthetic division.

Given:

Dividend =

Divisor =

To find:

The remainder by using the synthetic division.

Solution:

We have,

Dividend =

The coefficients of dividend are 2, 5, -3. Write these elements in the top row of synthetic division.

Divisor =

The value of divisor is 0 at . So, write -3 on the left side of division.

Write down the first coefficient of dividend in bottom row, then multiply it by -3 and write the result below the next coefficient of dividend then add the coefficient and write the result in bottom row, then repeat the steps up-to last coefficient.

-3    |        2          5         -3

      |                    -6         3

------------------------------------------

               2         -1           0

-----------------------------------------

Here, the first two elements of the bottom row represent the coefficient of quotient and last element represent the remainder.

Therefore, the remainder is 0.

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