Answer: The remainder will be 12.
Step-by-step explanation:
Since we have given that
[tex]f(x)=(2x^3+4x^2 -32x+18)[/tex]
And [tex] g(x)=x-3[/tex]
Now, we need to find the remainder while dividing f(x) by g(x).
So, by using "Remainder theorem" we get our answer.
[tex]g(x)=0\\\\x-3=0\\\\x=3[/tex]
Now, we use x=3 in f(x).
[tex]f(3)=2x^3+4x^2-32x+18\\\\f(3)=2(3)^3+4(3)^2-32(3)+18\\\\f(3)=2\times 27+4\times 9-96+18\\\\f(3)=54+36-96+18\\\\f(3)=12[/tex]
so, the remainder will be 12.
