Answer :
Given:
The function is:
[tex]f(x)=2x^3+2x^2-3x-3[/tex]
To find:
The remainder when the given function is divided by [tex]x-2[/tex].
Solution:
According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).
We have,
[tex]f(x)=2x^3+2x^2-3x-3[/tex]
This function is divided by [tex]x-2[/tex]. By using the remainder theorem, the remainder is f(2).
Putting [tex]x=2[/tex] in the given function, we get
[tex]f(2)=2(2)^3+2(2)^2-3(2)-3[/tex]
[tex]f(2)=2(8)+2(4)-6-3[/tex]
[tex]f(2)=16+8-9[/tex]
[tex]f(2)=15[/tex]
Therefore, the remainder is 15.