The question: The remainder obtained when 3x^4 + 7x^3 + 8x^2 -2x -3 is divided by x + 1 is?
The answer is 3. My book says to plug in -1 for x (which results with 3). Why should I do this?
Because that's the way you find a remainder.
For example if you want to solve the equation , in first instance you're going to search for a number wherefore , that means if you divide by you'll obtain remainder 0, in this case if you enter -1 you see so the remainder is 3. To have a closer look you can make the Horner scheme.
Hmm, thanks. Makes a little more sense. I guess I still need to work a few hands-on examples to make sense of why we do that. Let me ask a few questions to get a more thorough understanding:
1.) Why do we set the first equation equal to 0?
2.) Why does dividing by the the x-x1 give us remainder 0?