Using the reminder therom 4x^3+6x^2+3x+2 is divided by 2x + 3

-5/2 or - 2.5.

Step-by-step explanation:

The remainder theorem states that if the polynomial f (x) is divided by (x - a) then the remainder is f (a).

To find the remainder we put x = - 3/2 (by solving 2x + 3 = 0).

The remainder = 4 (-3/2) ^3 + 6 (-3/2) ^2 + 3 (-3/2) + 2

= - 27/2 + 27/2 - 9/2 + 2

= - 9/2 + 4/2

= - 5/2.