Concept

Factored Form

The result of factoring – writing a numeric or algebraic expression as the product of its factors – is called the factored form.

	Example	Factored Form
Natural Number	$6$	$2 \cdot 3$
Fraction	$\frac{4}{6}$	$\frac{2 \cdot 2}{2 \cdot 3}$
Polynomial	$x^{2} + 3 x + 2$	$(x + 2) (x + 1)$

The factored form has many uses, such as reducing fractions and finding the roots of a polynomial function, among others. Take care, however, of cases such as this:

x^{3} - 4 x \Leftrightarrow x (x^{2} - 4)

Although the original expression has been rewritten as a product of two factors, it has not been fully factored; therefore, it is a factored form of the expression, but the factored form of the expression would be written as

x (x + 2) (x - 2) .

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