Writing a polynomial in standard form means putting the term with the highest exponent first. The other terms with lower exponents are written in descending order.
Know MoreAn example of a polynomial in standard form is x^8 + 2 x^6 + 4 x^3 + 2x^2 + 3x - 2. In this example, there are terms with exponents and a constant. In the given polynomial, "x" is a variable, and the term "x^8" has the highest exponent, which is 8. This is also called the degree of the polynomial. The next term that follows is "2x ^6," which has the lower exponent of 6. The other terms in this polynomial are in descending order when looking at the exponents.
When writing a polynomial in standard form, it is important to look at each term to identify the exponents from highest to lowest correctly. The constant term, a number by itself, goes last in the standard form of polynomials.
Learn more about AlgebraPolynomial operations are basic math operations performed with polynomials instead of integers. A polynomial is an algebraic expression with more than one term. While there are algebraic polynomial operations, simple operations such as addition, multiplication, subtraction and division are also examples of polynomial operations.
Full Answer >The leading coefficient is the number that multiplies a variable to the highest degree in the expression. Because polynomials are arranged by degree from highest to lowest, the leading coefficient is the first number that appears in the expression, unless the coefficient is 1.
Full Answer >Factoring completely is an algebraic process that incorporates the three common factoring techniques: the greatest common factor, trinomials and the difference between two squares. These techniques by themselves often factor a polynomial into a single pattern, while factoring completely utilizes them together to simplify an expression as much as possible.
Full Answer >A monic polynomial is a mathematical expression that consists of coefficients and a single variable, with the leading coefficient equal to one. The leading coefficient is found in the term that contains the variable with the highest degree or exponent.
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