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# Polynomials

### Vocabulary for Algebra I - Exponents and Polynomials

Question | Answer |
---|---|

Zero Exponent | Any nonzero number raised to the zero power is 1 |

Negative Exponent | A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the corresponding positive exponent. |

Scientific Notation | a method of writing numbers that are very large or very small in two parts - a number between 1 & 10 that is multiplied by ten raised to a positive or negative power |

An exponential expression is completely simplified if... | 1) there are no negative exponents 2) the same base does not appear more than once in a product or quotient 3) no powers, products or quotients are raised to powers 4) numerical coefficients in a quotient do not have any common factor other than 1 |

Product of Powers Property | The product of two powers with the same base equals that base raised to the sum of the powers |

Power of a Power Property | A power raised to another power equals that base raised to the product of the exponents |

Power of a Product Property | A product raised to a power equals the product of each factor raised to that power |

Quotient of Powers Property | The quotient of two nonzero powers with the same base equals to base raised to the difference of the exponents |

Positive Power of a Quotient Property | A quotient raised to a positive power equals the quotient of of each base raised to that power |

Negative Power of a Quotient Property | A quotient raised to a negative power equals the reciprocal of the quotient raised to the opposite (positive) power |

Root Index | the small number to the left of the radical symbol that tells you which root to take - 2 would be square root, 3 would be cube root, etc. |

Factional Exponent 1/n | A number raised to the power of 1/n is equal to the "n"th root of that number |

Factional Exponent m/n | A number raised to the power of m/n is equal to the "n"th root of the number raised to the "m"th power |

Monomial | A number, a variable or a product of numbers and variables with whole-number exponents |

Degree of a Monomial | The sum of the exponents of the variables in a monomial |

Polynomial | A monomial or a sum or difference of monomials |

Degree of a Polynomial | The degree of the of the term with the greatest degree |

Standard Form of a Polynomial | Contains one variable and is written in with the terms in order from greatest degree to least degree |

Leading Coefficient | When written in standard form, it is the coefficient of the first term |

Linear Polynomial | Polynomial with the degree of 1 |

Quadratic Polynomial | Polynomial with the degree of 2 |

Cubic Polynomial | Polynomial with the degree of 3 |

Binomial | Polynomial with two terms |

Trinomial | A polynomial with three terms |

FOIL | A method for multiplying binomials: F - multiply first terms O - multiply outside terms I - multiply inside terms L - multiply last terms |

Perfect Square Trinomial | A trinomial that results from squaring a binomial |

Created by:
gklee