Question

Divide the polynomial 2x³+9x²+15x+9 by 2x+3.

Answer 1

When we divide the polynomial, 2x³ + 9x² + 15x + 9 by 2x + 3, the result obtained is x² + 3x + 3

How to divide the polynomial 2x³ + 9x² + 15x + 9 by 2x + 3?

The division of the plynomial, 2x³ + 9x² + 15x + 9 by 2x + 3 can be determined by using the long division method as illustrated below:

`&\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }x^2+3x+3\\2x+3 &\overline{\big)2x^3+9x^2+15x+9}\\&\text{ }\text{ }\text{ }\text{ }\text{ }&\underline{\text{ }-\ (2x^3+3x^2})\\&\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }6x^2+15x+9\\`

`&\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\underline{\text{ }-\ (6x^2+9x})}\\`

`&\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }6x+9\\&\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\underline{\text{ }-\ (6x+9})}\\&\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }0`

From the long division process shown above, we can conclude that when the polynomial, 2x³ + 9x² + 15x + 9 is divided by the expression, 2x + 3, the result obtained is x² + 3x + 3