Level 2 Certificate Mathematics · key term

Factor theorem

Definition

For a polynomial $f(x)$ , $f(r)=0$ if and only if $x-r$ is a factor of .

Specification 2.11 · Paper 1, Paper 2

The factor theorem lets us make this connection in both directions. We can use a known factor to identify a root, or use a root to discover a factor without first factorising the expression.
Revise: Factor Theorem

1
For a ‘show that’ question, display the substitution, simplify it to exactly zero, then state the conclusion using the factor theorem.

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x

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r

f(x)

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