Question

Find the quotient when the polynomial $x+3$ is divided by $x+1$ using synthetic division method.

• A. 0
• B. 1
• C. 3
• D. 2

Answer 1

The correct option is B 1

Index form of the dividend polynomial is :

$x+3$

Coefficient form of the dividend polynomial is :

(1,3)

Divisor polynomial =x+1

Steps:
1. Draw the horizontal and vertical lines as below :



2. Divisor is x+1. Take opposite number of 1 which is -1.Write -1 to the left of the vertical line. Write the coefficient form of the dividend polynomial in the first row and write the first coefficient as it is in the third row

$\begin{array}{ccccc}& x^1& x^0& & \\ & 1& 3& & \\ -1& \downarrow & & & \\ & 1& & & \end{array}$

3. The product of 1 in the third row
with divisor -1 is -1. Write this -1 in the second row and second column below the coefficient 3. Addition of 3 and -1 which is 2, is to be written in the third row and second column.


$\begin{array}{ccc}& x^1& x^0\\ & 1& 3\\ -1& \downarrow & -1\\ & 1& |-2\end{array}$

The last addition is the remainder, which is ' 2 '.

The coefficient form of the quotient is (1).

So, quotient is 1, remainder is ' 2 '