factorise

Thân thiện

The student factorises the quadratic equation on the whiteboard.

Definition

1. Verb:
   • To resolve (a polynomial) into factors: The mathematical process of breaking down a polynomial expression into a product of simpler polynomials or factors. This is the reverse operation of expanding expressions.

Usage

• The verb "factorise" is used primarily in mathematics, specifically in algebra. It describes the action of finding the factors of a polynomial. It is a transitive verb, requiring a direct object (the polynomial to be factorised).
• In American English, the spelling "factorize" is more common, but both forms are correct.

Examples

• Verb:
  • The student was asked to factorise the quadratic equation x² + 5x + 6.
  • Can you factorise this expression completely?
  • The first step in solving the equation is to factorise the polynomial.

Advanced Usage

• "To factorise out": To remove a common factor from all terms of an expression.
  • You can factorise out the greatest common factor to simplify the expression.

Variants and Related Words

• Factorization / Factorisation (n): The process or result of factorising.
  • The factorization of the polynomial revealed its roots.
• Factor (n): A number or algebraic expression that divides another number or expression evenly.
• Factor (v): A more general verb meaning to include something as a relevant element or to resolve into factors.
• Factorable (adj): Capable of being factorised.

Synonyms

• Resolve into factors: A more formal phrase with the same meaning.
• Decompose: In a mathematical context, can sometimes be used similarly, though it is more general.

Related Phrases

• Common factor: A factor shared by all terms in an expression.
• Prime factorisation: The process of breaking a number down into its prime factors (a related but distinct concept from polynomial factorisation).

Học thuật

Verb

1. resolve (a polynomial) into factors

Từ đồng nghĩa

• factorize