Question

How do I divide this?
`\frac{2 {x}^(3) + 3 {x}^(2) + 2 }{x + 2}`

Answer 1

From the given problem,

`(2x^3+3x^2+2)/(x+2)`

Using synthetic division to find the quotient of the expression.

Reaarrange first the expression based on the degree from highest to smallest.

As you notice, there is no x^1 term, so we will add 0x.

`(2x^3+3x^2+0x+2)/(x+2)`

Take the coefficients of the numerator then proceed to use the synthetic division.

The coefficients are 2, 3, 0 and 2

The last number at the lower left will be the remainder and the coefficients of the quotient are 2, -1 and 2

This will be :

`2x^2-x+2-(2)/(x+2)`

Note that the remainder is written as r/divisor

r = -2 and the divisor is x+2

Therefore, the answer is :

`2x^2-x+2-(2)/(x+2)`