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From the given problem,
[tex]\frac{2x^3+3x^2+2}{x+2}[/tex]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.
[tex]\frac{2x^3+3x^2+0x+2}{x+2}[/tex]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 :
[tex]2x^2-x+2-\frac{2}{x+2}[/tex]Note that the remainder is written as r/divisor
r = -2 and the divisor is x+2
Therefore, the answer is :
[tex]2x^2-x+2-\frac{2}{x+2}[/tex]