Question

Find the remainder when f(x) = 2x3 – 12x2 + 11x + 2 is divided by x – 5.

Answer 1

The remainder of the function divided by a factor can be obtained by substituting the factor to the function. In this case, we substitute 5 to the x in the expression 2x3 – 12x2 + 11x + 2. The answer is equal to 7. The answer hence to this problem is C 

Answer 2

When dividing polynomial f(x) by linear polynomial x-a, the remainder is equal to f(a).

In your case a=5. Find f(a)=f(5):

$f(5) = 2\cdot 5^3 - 12\cdot 5^2 + 11\cdot 5 + 2=2\cdot 125-12\cdot 25+55+2=250-300+55+2=7.$

Answer: correct choice is C.