Question

Find the remainder when f(x) is divided by (x - k).

f(x) = 3x4 + 11x3 + 2x2 - 7x + 61; k = 3

Answer 1

Synthetic division:

3   |   3   11    2      -7      61
.    |         9   60   186    537
- - - - - - - - - - - - - - - - - - - -
.    |   3   20  62   179    598

which translates to

$\dfrac{3x^4+11x^3+2x^2-7x+61}{x-3}=3x^3+20x^2+62x+179+\dfrac{598}{x-3}$

i.e. you're left with a remainder of 598.