Question

Find the quotient when $6x^3+4x^2+2$ is divided by $x-2$ using synthetic division method.

• A. $12x^2+16x+32$
• B. $6x^2+16x+32$
• C. $6x^2+16x+66$
• D. $6x^2+16x+32$

Answer 1

The correct option is B $6x^2+16x+32$

Index form of the dividend polynomial is :

$6x^3+4x^2+2=6x^3+4x^2+0x+2$

Coefficient form of the dividend polynomial is :
(6,4,0,2)

Divisor polynomial = x-2

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



2. Divisor is x-2. Take opposite number of -2 which is 2. Write 2 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

$\begin{array}{ccccc}& x^3& x^2& x^1& x^0\\ & 6& 4& 0& 2\\ 2& \downarrow & & & \\ & 6& & & \end{array}$

3. The product of 6 in the third row
with divisor 2 is 12. Write this 12 in the second row below the coefficient 4. Addition of 4 and 12 which is 16, is to be written in the third row.

Similarly by multiplying and adding, we have

$\begin{array}{ccccc}& x^3& x^2& x^1& x^0\\ & 6& 4& 0& 2\\ 2& \downarrow & 12& 32& 64\\ & 6& 16& 32& |-66\end{array}$

The last addition is the remainder, which is '66 '.

The coefficient form of the quotient is (6, 16, 32).

So, quotient is $6x^2+16x+32$, and the remainder is '66'.