1. Introduction: You Already Know This From Class 4
Think back to plain number division. You have 17 toffees. You want to share them among 5 friends, equally.
Each friend gets 3 toffees. That uses up 15. Two toffees are left over.
We write this as:
17 = 5 × 3 + 2
Stop scrolling. Read that line again before moving on.
Four things are sitting in that line, and each has a name you have heard before:
- 17 is the dividend — the thing being divided.
- 5 is the divisor — the thing you divide by.
- 3 is the quotient — how many full shares came out.
- 2 is the remainder — what is left, too small to share again.
Now notice one quiet rule. The remainder is 2, and the divisor is 5. The remainder is smaller than the divisor. It has to be. If 5 toffees were still left, you could give one more to each friend.
You can now read any division as: dividend = divisor × quotient + remainder.
Okay, so far we have seen this with numbers. Now we move to polynomials — and the surprise is that the same four words and the same rule carry over, almost unchanged.