Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

Polynomials

13 min read

Expanding and factorising, polynomial division, and the remainder and factor theorems.

Polynomials are expressions like $ax^3 + bx^2 + cx + d$ . Two theorems make them easy to factorise.

The remainder theorem

When a polynomial $f(x)$ is divided by $(x - a)$ , the remainder is $f(a)$ .

Worked example. $f(x) = x^3 - 2x + 4$ divided by $(x - 2)$ leaves $f(2) = 8 - 4 + 4 = 8$ .

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Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

13 min read

Expanding and factorising, polynomial division, and the remainder and factor theorems.

Polynomials are expressions like $ax^3 + bx^2 + cx + d$ . Two theorems make them easy to factorise.

When a polynomial $f(x)$ is divided by $(x - a)$ , the remainder is $f(a)$ .

Worked example. $f(x) = x^3 - 2x + 4$ divided by $(x - 2)$ leaves $f(2) = 8 - 4 + 4 = 8$ .

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.