Divide x^4+3x^3-2x^2+4 by x-2
which answer shows the correct synthetic division and quotient

Answer:
option-A
[tex]\frac{x^4+3x^3-2x^2+4}{x-2}=x^3+5x^2+8x+16+\frac{36}{x-2}[/tex]
Step-by-step explanation:
we are given
divisor is
[tex]=x^4+3x^3-2x^2+4[/tex]
Dividend is
=x-2
so, we can use synthetic division
so, we can write our expression as
[tex]\frac{x^4+3x^3-2x^2+4}{x-2}=x^3+5x^2+8x+16+\frac{36}{x-2}[/tex]
so,
option-A