A monomial is an expression in algebra that contains one term, like 3xy. Monomials include numbers, whole numbers and variables that are multiplied together, and variables that are multiplied together. A polynomial is a sum of monomials where each monomial is called a term. Read more about the difference between monomials and polynomials, the rules for each term and several helpful examples. Identifying a MonomialFinding a monomial is easier than it seems. "Mono" means one, meaning that "monomial" includes only one term. It is a piece of a polynomial. Monomials can include these characteristics:
Monomials cannot have a fractional or negative exponent. Monomial examples include:
A monomial multiplied by a monomial is also a monomial. A monomial multiplied by a constant (not variable) is also a monomial. When looking at examples of monomials, you need to understand different types of polynomials, which have more than one term (since "poly" means "many.") Following is an explanation of polynomials, binomials, trinomials, and degrees of a polynomial. Identifying a PolynomialA polynomial shows the sum of monomials. It is an algebraic expression with a finite number of terms. Because a polynomial is made of monomials, it also cannot have negative exponents. Polynomial examples include:
Types of PolynomialsIf you notice that these polynomials have different terms, that's because they're different types of polynomials.
When a polynomial has four terms (such as 5x6 - 17x2 + 97 + 24x), it's sometimes called a quadrinomial. However, larger polynomials are usually known as four-term polynomials, five-term polynomials, and so on. Degrees of Monomials and PolynomialsThe degree of a monomial or polynomial is the highest power of the variable in that polynomial, as long as there is only one variable. If there is more than one variable, you add up the exponents for all the variables to find the degree. If a polynomial has more than one variable, then you can find the degree of by looking at each monomial. For example: 14x4 + 27x2y - y has the degree of 4. Looking at each individual term, you find that the exponents are 4, 3 (2+implicit 1), and 1). 4 is the highest, so the degree is 4. For example:
Degrees of Polynomial TermsA second degree polynomial (such as 6x2 + 13x + c) is also called a “quadratic.” You may wonder where the word “quadratic” comes from, because the prefix “quad” usually stands for four. The word comes from the Latin word for “making square.” So, in this instance, “quad” refers to the four corners of a square. A third degree polynomial is called a “cubic”, a fourth degree is called a "quartic", and a fifth degree polynomial is called a "quintic." Sixth degree polynomials are "sextic" and seventh degree polynomials are "septic." Algebra Means RestorationAlgebra, which is Arabic for "restoration," is a branch of pure mathematics. Pure mathematics differs from other disciplines because it is not necessarily applied to any particular situation, but it investigates the concepts and beauty of math itself. The history of algebra is enriching as well; from the ancient mathematical tablets of Babylon to the classical days of Diophantus, Greek mathematician and writer of Arithmetica, and the Medieval discovery of algebra itself by the "father of algebra," Al-Khwarizmi (whose name was the inspiration for the word algorithm.), algebra is a way to bring balance to mathematics. What is the degree of the monomial?The degree of the monomial is the sum of the exponents of all included variables.
What is the degree of the monomial 4?Answer and Explanation: The degree of the monomial 4g is 1. The monomial 4g is a monomial in one variable, g .
What is the degree of monomial 3x 2y 3?The degree of the monomial 3x2y3 is 5. The degree of a monomial is defined as the sum of the exponents of the variables in the monomial. Therefore, the degree of 3x2y3 is equal to the sum of the exponents of the variables, x and y, in the monomial.
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