Sec 3 students will be having quizzes on Remainder and Factor Theorem soon, and that means it is time for some revision! If Remainder and Factor doesn’t ring a bell, or you need a quick checklist of things to revise – we’ve got just the thing for you! Make sure not to miss out on our summary notes and practice questions below!

**What is Remainder and Factor Theorem?**

Remainder and Factor Theorem is an extension of topics which you should already know, building upon what you have learnt in **basic algebra**, polynomials, and functions.

Remainder and Factor Theorem comes in handy when we are trying to divide polynomials. The manual way for dividing polynomials is by long division. Recall that primary school method of dividing a big number?

Let keep it simple and say that we want to divide P by Q, and any remainder is R.

When you divide P and it leaves no remainder (R=0), it means that the Q is a factor of the original number. The same logic applies to polynomials.

We are sometimes interested to find the factors of polynomials because then it helps us find the roots of the polynomials. We can draw a relationship between remainder and factor by understanding that when the R=0, Q(x) is a factor of P(x) – this is the **Factor Theorem**.

Since the remainder of a polynomial can be informative to us, mathematicians found a way to skip the long division and just find the remainder. That formula is given in the **Remainder Theorem**.