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.