Question

Use the long division method to find the result when 9x^3+18x^2+20x+169x 3 +18x 2 +20x+16 is divided by 3x+43x+4.

Answer 1

Given:

Dividend = $9x^3+18x^2+20x+16$

Divisor = $3x+4$

To find:

The quotient and remainder by using the long division method.

Solution:

Using the long division method, divide the polynomial $9x^3+18x^2+20x+16$ by $3x+4$ as shown below:

$3x+4 |\overline{9x^3+18x^2+20x+16}|3x^2+2x+4$

         $9x^3+12x^2\\\underline{(-)\quad (-)\quad \quad \quad}$

             $0+6x^2+20x$

                   $6x^2+8x\\\underline{(-)\quad (-)\quad \quad \quad}$

                       $0+12x+16$  

                             $12x+8\\\underline{(-)\quad (-)}$

                                     $\underline{\quad 0\quad}$

Therefore, the quotient is $3x^2+2x+4$ and the remainder is 0.