monic polynomial
- noun
- /ˈmɒnɪk pəˈlɪnəˌmiəl/
- Specialized
:
polinomio monico
- A monic polynomial has a leading coefficient of 1.
Examples
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When solving equations, mathematicians often prefer to work with a monic polynomial for simplicity.
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The equation is a monic polynomial of degree 3.
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A monic polynomial has a leading coefficient of exactly one, making it unique among polynomials.
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Every irreducible monic polynomial plays a key role in field theory.
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A monic polynomial is defined as a polynomial whose leading coefficient equals one.
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In algebra, converting a polynomial into a monic polynomial simplifies many calculations.
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For any quadratic equation, the standard form also includes a monic polynomial.
Surface Forms
Morphology
monic + polynomial
The adjective "monic" is a specialized mathematical term whose technical meaning ('leading coefficient = 1') is not transparently recoverable from the general noun "polynomial". A B1 learner who knows only the surface constituents (and perhaps the prefix mono-) would not reliably infer the specific property about the leading coefficient without domain knowledge. This makes the compound effectively idiomatic/technical and opaque to typical learners.
Etymology
Monic polynomial comes from a word meaning 'one'. It names a polynomial whose leading coefficient, the number before the highest power, is exactly '1', so the polynomial begins with '1' and is easier to work with.
