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


`(3x^4+11x^3+2x^2-7x+61)/(x-3)=3x^3+20x^2+62x+179+(598)/(x-3)`

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