Given:
Dividend = [tex]9x^3+18x^2+20x+16[/tex]
Divisor = [tex]3x+4[/tex]
To find:
The quotient and remainder by using the long division method.
Solution:
Using the long division method, divide the polynomial [tex]9x^3+18x^2+20x+16[/tex] by [tex]3x+4[/tex] as shown below:
[tex]3x+4 |\overline{9x^3+18x^2+20x+16}|3x^2+2x+4\\[/tex]
[tex]9x^3+12x^2\\\underline{(-)\quad (-)\quad \quad \quad}[/tex]
[tex]0+6x^2+20x[/tex]
[tex]6x^2+8x\\\underline{(-)\quad (-)\quad \quad \quad}[/tex]
[tex]0+12x+16[/tex]
[tex]12x+8\\\underline{(-)\quad (-)}[/tex]
[tex]\underline{\quad 0\quad}[/tex]
Therefore, the quotient is [tex]3x^2+2x+4[/tex] and the remainder is 0.
