factorize
Học thuậtThân thiện
Definition
- Verb:
- To resolve (a polynomial) into factors: To express a polynomial as a product of its factors, which are polynomials of lower degree. This is a fundamental operation in algebra.
Usage
- The verb factorize is used primarily in mathematics, specifically in algebra. It describes the process of breaking down a complex polynomial expression into simpler multiplicative components (factors).
- It is a transitive verb, requiring a direct object (the polynomial to be factorized).
- Common contexts include solving equations, simplifying expressions, and finding roots.
Examples
- Verb:
- The student learned how to factorize quadratic equations.
- Can you factorize the expression
x² - 5x + 6? - The first step is to factorize the polynomial completely.
Advanced Usage
- "To factorize over the integers/rationals/reals": Specifies the number system (the set of numbers) within which the factors must be expressed.
- The polynomial
x² - 2cannot be factorized over the rational numbers, but it can be factorized over the real numbers.
- "To factorize completely": To break down the polynomial into irreducible factors (factors that cannot be broken down further within a given number system).
- Your final answer must show the polynomial factorized completely.
Variants and Related Words
- Factorization (n): The process or result of factorizing.
- The factorization of
x² - y²is(x - y)(x + y).
- Factor (n/v): As a noun, a component that multiplies with others; as a verb, a more general term meaning to resolve into factors, often used interchangeably with .
- One factor of
12is3. (n) - We need to factor this expression. (v)
Synonyms
- Factor (v): To resolve into factors. (Note: In many contexts, and are synonyms, though is often preferred for polynomials.)
- Resolve into factors: A more descriptive phrase with the same meaning.
Related Phrases (Phrasal Verbs)
(Not commonly applicable for this technical mathematical term.)
Related Idioms
(Not commonly applicable for this technical mathematical term.)
Verb
- resolve (a polynomial) into factors