The result of dividing [tex]15x^{3}+x^{2}-3x+2[/tex] by [tex]3x+2[/tex] is [tex]5 x^{2} -3x+1[/tex] with no remainder. Please check the step by step procedures in the picture attached.
We can conclude that:
The quotient of the division is [tex]5 x^{2} -3x+1[/tex]
The remainder of the division is [tex]0[/tex]
The divisor is [tex]3x+2[/tex]
The dividend is [tex]15x^{3}+x^{2}-3x+2[/tex]