The remainder and factor theorems and cubic equations
Watch the whole lecture free
Make a free account to watch every lecture to the end: 2 worked examples, 4 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
That was the teaching part. The rest of this lecture is free with an account: 2 worked examples, 4 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
No password needed now: we email you a link to set one. Already have an account? Sign in, then come back to this page.
The teaching part (1 min) is free to watch. A free account opens the whole lecture: 2 worked examples, 4 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- A shortcut for long division
- The remainder theorem
- The factor theorem
Read the transcript of the teaching part
Last time
Before we start: last time, in Quadratic inequalities, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
A shortcut for long division
Long division of a cubic is slow and easy to get wrong. But if you only want the remainder, or only want to know whether a bracket is a factor, you can skip the division. Just substitute one number.
The remainder theorem
When a polynomial p of x is divided by x minus a, the remainder is p of a. For a bracket like x plus two, a is minus two. Read the sign carefully. For a bracket like two x minus one, set it to zero. Then x is one half, and the remainder is p of one half.
The factor theorem
If p of a equals zero, there is no remainder, so x minus a is a factor. And the other way round. If x minus a is a factor, then p of a is zero. This gives you equations for unknown constants.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Factorising a cubic · The remainder and factor theorems.
The whole chapter: Factors of Polynomials, Simultaneous Equations.
Chapter 3: Factors of polynomials
- The remainder and factor theorems and cubic equations 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.