Question

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

• A. $4x^2+9x+18$
• B. $4x^2+9x+22$
• C. $5x^2+9x+18$
• D. $4x^2+7x+18$

Answer 1

The correct option is A $4x^2+9x+18$

Index form of the dividend polynomial is :

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

Coefficient form of the dividend polynomial is :

(4,1,0,-3)

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

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

3. The product of 4 in the third row
with divisor 2 is 8. Write this 8 in the second row below the coefficient 1. Addition of 1 and 8 which is 9, is to be written in the third row.

Similarly by multiplying and adding, we have

$\begin{array}{ccccc}& x^3& x^2& x^1& x^0\\ & 4& 1& 0& -3\\ 2& \downarrow & 8& 18& 36\\ & 4& 9& 18& |-33\end{array}$

The last addition is the remainder, which is ' 33 '.

The coefficient form of the quotient is (4, 9, 18).

So, quotient is $4x^2+9x+18$, remainder is '33'