Verified Answer :

It is to be solved by reminder thorem
f(x)/(x-k) will have reminder f(k), 
so, f(2) = 5(2^4) + 8 (2^3) +4 (2^2) -5(2) +67

             =516 + 88 +44 -5*2 +67
             =80 + 64 + 16 -10 +67

             = 217

Answer: The remainder when f(x) is divided by (x-2) is 217.

Step-by-step explanation:

Since we have given that

\(f(x) = 5x^4 + 8x^3 + 4x^2 - 5x + 67\)

And it is divided by g(x)=(x-k)

Here, k= 2

So, g(x)= x-2

So, we need to find the remainder .

By using "Remainder theorem ":

\(Put\ g(x)=0\\\\x-2=0\\\\x=2\)

Now,

\(f(2)=5(2)^4 + 8(2)^3 + 4(2)^2 - 5(2) + 67\\\\f(2)=80+64+16-10+67\\\\f(2)=217\)

Hence, the remainder when f(x) is divided by (x-2) is 217.

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