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Concept

Factoring

Given the product of a multiplicative expression, factoring is the process of breaking a number down into its smaller factor components. For example, the integer

12

can be factored in several different ways:

12 = 12 = 12 = 2 \cdot 6 3 \cdot 4 2 \cdot 2 \cdot 3

Similarly, multiplicative algebraic expressions, such as

4 x^{3},

can be rewritten by rewriting their coefficients and variables as a product of their factors.

4 x^{3} = 2 \cdot 2 \cdot x \cdot x \cdot x

The prime factorization of a multiplicative expression occurs when all of its factors are prime. This is true for both prime numbers and prime polynomials.

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