Question

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

Answer 1

Given:

Dividend =
`2x^2+5x-3`

Divisor =
`x+3`

To find:

The remainder by using the synthetic division.

Solution:

We have,

Dividend =
`2x^2+5x-3`

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

Divisor =
`x+3`

The value of divisor is 0 at
`x=-3`. 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.