Answer: Second option is correct.
Explanation:
Since we have given that
[tex]f(x)=3x^4+2x^3-x^2+2x-19[/tex]
And [tex]g(x)=x+2[/tex]
To find the remainder, we use the Remainder Theorem, which states that when f(x) is divided by (x-c) then the f(c) is the required remainder.
So,
Here, we have,
[tex]x+2=0\\\\x=-2[/tex]
So, we will find f(-2) which will give us the required remainder,
[tex]f(-2)=3(-2)^4+2(-2)^3-(-2)^2+2(-2)-19\\\\f(-2)=(3\times 16)-(2\times 8)- 4-4-19\\\\f(-2)=48-16-36-4-19\\\\f(-2)=5[/tex]
Hence, Second option is correct.
