# monic

A *monic polynomial ^{}* is a polynomial

^{}with a leading coefficient of 1. That is, if ${P}_{n}(x)$ is a polynomial of degree $n$ in the variable

^{}$x$, then the coefficient of ${x}^{n}$ in ${P}_{n}(x)$ is 1.

For example, ${x}^{5}+3{x}^{3}-10{x}^{2}+1$ is a monic 5th-degree polynomial. $3{x}^{2}+2z-5$ is a 2nd-degree polynomial which is not monic.

Title | monic |
---|---|

Canonical name | Monic1 |

Date of creation | 2013-03-22 12:18:42 |

Last modified on | 2013-03-22 12:18:42 |

Owner | akrowne (2) |

Last modified by | akrowne (2) |

Numerical id | 9 |

Author | akrowne (2) |

Entry type | Definition |

Classification | msc 12E10 |

Synonym | monic polynomial |

Related topic | EisensteinCriterion |

Related topic | IrreduciblePolynomial2 |

Related topic | AlgebraicInteger |