Question

If we divide the polynomial x4 + 4x^3 + 2x^2 + x + 4 by x^2 + 3x, what will be the remainder?

Answer 1

Let's find out! What's the first term of \(x^4+4x^3+2x^2+x+4\) divided by the first term of \(x^2+3x\)?

Answer 2

x^2?

Answer 3

this is the answer that I got for the problem, but I am not sure if it is correct:
x^2+x−1+(4x+4/x^2+3x)

Answer 4

That's right, the remainder is \(4x+4\), and the whole quotient would be \[x^2+x-1+\frac{4x+4}{x^2+3x}\]