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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
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