# Remainder Theorem

**Question**

What is the remainder of the function f(x) = 2×2 + 2x + 5 when it is divided by the following linear factor?

- x – 1
- x + 1
- 1 – 3x

**Answer**

- 9
- 5
- 53/9

*Note:*

When a polynomial, g(x) is divided by a linear factor, (x-b), where b is equal to number. It will results a quotient q(x) with possible a reminder of r(x).

The relationship between f(x), linear factor, quotient and the remainder can be written as follow.

g(x) = Quotient * (1/Linear Factor) + Remainder

Since dividing g(x) by (x-b) will results a remainder of r(x). Thus,

g(b) = Remainder

If g(b) = 0, then x-b is a factor of the function (factor theorem).

## About the Math Tutor - Dr Loo

I am a PhD holder with 9 years of teaching experience at secondary school and university. My expertizes are mathematics, statistics, econometrics, finance and machine learning.

Currently I do provide consultation and private tuition in Singapore. For those who are looking for math tutor in Singapore or statistics tutor in Singapore, please feel free to contact me at +65-85483705 (SMS/Whatsapp/Telegram).

Some of the math tuition in Singapore I provide includes O-level math tuition and also JC Math Tuition (H1 Math Tuition & H2 Math Tuition). On the other hand, my statistics tuition in Singapore mostly focus on pre-university level until postgraduate level. For those who prefer online tutoring service, the online O-level math tuition and online JC math tuition are also available.

## For those who are looking for math tution in Singapore

Need help with this topic? I do provide mathematics home tuition in Singapore for O-level math and also JC H2 math. In addition, online math tutoring is available as well. Feel free to contact me if you would like to know further.