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.
Summary notes
In our IP Math tuition classes, we help our students review the topics before their quizzes through the use of skills checklists and mock tests. A skills checklist is more than a formula sheet – it lists down the essential concepts you need to know for any given topic, such as the techniques for solving questions. If you browse through the checklist and find anything that looks unfamiliar, it is a sign that you should go back to your notes and master that concept before progressing to do any mock papers.
Here is our summary checklist for Remainder and Factor Theorem:
Practice questions
Once students at our tuition centre in Singapore are fairly familiar with the skills, we encourage them to familiarise themselves with applying them to questions using practice questions. During the learning stage, we recommend doing similar types of questions which target one skill at a time, so you can focus on mastering that concept before you move on.
Only when you feel quite confident with all the concepts, should you attempt a mock test – which typically mixes question types and topics. These helps you practice identifying question types and works on your time management skills.
Feel free to try out these questions as part of your revision for Remainder and Factor Theorem!
Expert guidance
With the proper resources, you can revise and practice on your own at home without a tutor. However, our students find it most beneficial when they can consult our tutors directly about any questions they have. Many times, our tutors are able to pinpoint mistakes and suggest new ways of understanding a concept which saves our students plenty of precious time. As it is easy to have blindspots when reviewing your own work, having an expert perspective is always helpful!
Conclusion
Remainder and Factor Theorem is not a very major topic, but it intersects with other important topics and concepts like factors, roots, polynomials, and functions. If you want to do well in Math, it is not a topic you should be taking lightly!
We hope our summary notes and practice questions give you a little boost in your revision towards your quiz. If you attend our Sec 3 Math Tuition, our tutors are also always ready to address your queries and offer advice! All the best for your upcoming quiz!