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For the purpose of this definition, consider a polynomial as an expression that is made up of variables and constants, and whose exponents of the variables are only positive integer numbers rather than fractions. The polynomial terms are mostly separated by addition or subtraction operators, with a few exceptions. Polynomials are used in a variety of applications, including the formulation of polynomial equations and the definition of polynomial functions. The expression x2+2x-3 is an example of a polynomial expression. Due to the fact that the term with the highest power of ‘x’ is ‘x2’, this polynomial has a degree of 2. There are three terms in this polynomial. Polynomials can be divided into two groups based on the total number of terms and the degree of the polynomial.
The variables in polynomials have only non-negative integer powers, and the variables are expressed as algebraic expressions. For example, the polynomial 5×2 – x + 1 can be written as It is not a polynomial in the algebraic expression 3×3 + 4x + 5/x + 6×3/2 because one of the powers of ‘x,’ the power of 3, and the power of 4, are fractions, and the other is negative. Polynomials are expressions that contain one or more terms that have a non-zero coefficient in their coefficients. Variables, exponents, and constants are included among the terms. The leading term of a polynomial is the first term that appears in the polynomial. A standard polynomial is one in which the first term has the highest degree, and the subsequent terms are arranged in descending order of the powers or exponents of the variables, followed by constant values, until the highest degree is reached. The coefficient is a number that has been multiplied by a specific variable. A constant is a number that does not have any variables associated with it.
Types of polynomials based on degree:
The degree of a polynomial is defined as the highest power of the leading term or the highest power of the variable in the polynomial. This is achieved by arranging the polynomial terms in the descending order of their powers before multiplying them together. They can be divided into four major types based on the degree of the polynomial being considered. They are, in fact.
Zero or Constant polynomial
Linear polynomial
Quadratic polynomial
Cubic polynomial
Types of polynomials | Meaning | Examples |
Zero or constant polynomial | A zero polynomial is a polynomial that has exactly zero degrees. | 3 or 3×0 |
Linear polynomial | Linear polynomials are polynomials that have the degree of one as the degree of the polynomial. The highest exponent of the variable(s) in a linear polynomial is 1, and the lowest exponent is 0. | x + y – 4, 5m + 7n, 2p |
Quadratic polynomial | Quadratic polynomials are polynomials with the degree of 2 as the degree of the polynomial in question. | 8×2 + 7y – 9, m2 + mn – 6 |
Cubic polynomial | Cubic polynomials are polynomials that have the number three as the degree of the polynomial. | 3×3,
p3 + pq + 7 |
Types of polynomials based on terms:
There are several different types of polynomials based on the number of terms they contain. There are polynomials with one term, polynomials with two terms, polynomials with three terms, and even more terms. Polynomials are classified into the following categories based on the number of terms:
Monomials:
When a polynomial expression contains only one term, it is referred to as a monomial expression. For instance, 4t, 21x, 2y, and 9pq. Apart from that, the sum of 2x, 5x, and 10x is a monomial because these are like terms that when added together result in 17x.
Binomials:
In contrast to terms, a binomial is a polynomial with only two terms. For example, 3x + 4×2 is a binomial because it contains two unlike terms, namely 3x and 4×2, and 10pq + 13p2 is a binomial because it contains two unlike terms, namely 10pq and 13p2.
Trinomials:
In contrast to terms, a trinomial is a polynomial with three factors. For example, 3x + 5×2 – 6×3 and 12pq + 4×2 – 10 are both trinomials.
A polynomial expression can contain more than three terms at the same time. Four-term polynomials are polynomials that have four terms that are unlike each other. Polynomials with 5 terms, for example, are referred to as five-term polynomials, and so forth.
Conclusion:
A polynomial is an algebraic expression in which the variables involved have positive integral powers rather than negative integral powers. The polynomial terms are mostly separated by addition or subtraction operators, with a few exceptions. Polynomials are used in a variety of applications, including the formulation of polynomial equations and the definition of polynomial functions.
A standard polynomial is one in which the first term has the highest degree, and the subsequent terms are arranged in descending order of the powers or exponents of the variables, followed by constant values, until the highest degree is reached. The degree of a polynomial is defined as the highest power of the leading term or the highest power of the variable in the polynomial. They can be divided into four major types based on the degree of the polynomial being considered. They are, in fact.
Zero or Constant polynomial
Linear polynomial
Quadratic polynomial
Cubic polynomial
There are several different types of polynomials based on the number of terms they contain.
When a polynomial expression contains only one term, it is referred to as a monomial expression. In contrast to terms, a binomial is a polynomial with only two terms. In contrast to terms, a trinomial is a polynomial with three factors. A polynomial expression can contain more than three terms at the same time. Four-term polynomials are polynomials that have four terms that are unlike each other.
