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Module 1: Factors of polynomials

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Factorisation process for cubics

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Intermediate Mathematics - Factorisation process for cubics

Factorisation process for cubics

(a) Take out any common factors

(b)

For the general cubic polynomial _ax_ ² + _bx_² + _cx_ + _d_ look at the
coefficient ratios _a/b_ and _c/d_. If _a/b_ = _c/d_ then factorise after
first grouping the first two terms and last two terms.

(c) If (b) above does not apply, then use the Factor Theorem with long or
synthetic division.

(d) If difficulties arise finding the first factor using the Factor
Theorem, the graphics calculator could be used to find at least one of the
"zeros" at x=a , say. That means that (x-a) is one of the factors of P(x).

(e) Important identities

(f) Useful expansions

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