Given:
Dividend = [tex]2x^2+5x-3[/tex]
Divisor = [tex]x+3[/tex]
To find:
The remainder by using the synthetic division.
Solution:
We have,
Dividend = [tex]2x^2+5x-3[/tex]
The coefficients of dividend are 2, 5, -3. Write these elements in the top row of synthetic division.
Divisor = [tex]x+3[/tex]
The value of divisor is 0 at [tex]x=-3[/tex]. 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.
