Polynomials – Explanation, Formulas, and Types

If a mathematical expression or algebraic expression consists of coefficients and variables that are linked together by arithmetic operations such as multiplication, addition, subtraction, and positive integer exponentiation of variables is known as a polynomial. These expressions consist of variables that have whole number exponents or powers. Polynomials should not contain fractional, negative powers, or square roots of variables. There also should not be any variables in the denominators. Let us see a list of examples to strengthen our understanding of this concept.

• x² – 4x + 3 is a polynomial. 1 and 4 represent coefficients of the variables x² and x, 3 is the constant, and this polynomial is linked by addition, subtraction, multiplication, and exponentiation.
• 6y^-4 + 3 cannot be classified as a polynomial because the power of y is negative.
• √z is not a polynomial as it contains the square root of the variable z.

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Types of Polynomials

Polynomials can be classified based on the number of terms and the degree. 

Based on Degree

The highest exponential value that occurs in a polynomial is known as the degree of that polynomial. Another way of defining the degree of a polynomial is by looking at the highest value of exponents of the monomials within the polynomials. Let us now categorize the various polynomials on the basis of the degree.

• Zero Polynomial: A polynomial with the highest exponent value as 0 or degree = 0 is called a zero polynomial. E.g., 20.
• Linear Polynomial: If the highest degree of a monomial is 1, it is called a linear polynomial. E.g. 56z + 3
• Quadratic Polynomials: Such polynomials have the highest degree as 2. E.g. k² + 8k – 20
• Cubic Polynomial: When 3 is the highest value of a monomial in a polynomial, it is known as a cubic polynomial. E.g. f³ – 2f² + 1
• Quartic Polynomials: If 4 is the highest degree, it is called a Quartic Polynomial. E.g., 7p⁴

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Based on the Number of Terms

• Monomial: If a polynomial contains a single term in the algebraic expression, it is called a monomial. It should be noted that this solitary term should be non-zero. Examples of monomials are 7xy, 89y⁷, 20, etc.
• Binomial: If a polynomial contains exactly two terms in the expression, it is called a binomial. Two monomials combine to form a binomial expression. These monomials are linked together using either addition or subtraction. 5xs + 2j, v⁵f – g are examples of binomials as they have only two terms.
• Trinomial: When a polynomial has only three terms in the expression, it is called a trinomial. We can think of a trinomial as having either three monomials or a combination of one monomial and one binomial expression. z² + 4z + 4, p⁴q + m³c – 3 are trinomials.

Thus, based on the degree or number of terms, we can classify polynomials. A point to note is that the types do not just stop at quartic polynomials and trinomials. With an increase in the degree and increase in the number of terms, the divisions keep on increasing. However, this list is just to give an idea to the readers. Usually, for the purpose of school, we limit ourselves to the polynomials specified in the list.

Conclusion

Polynomials are used in every branch of Mathematics; hence, kids should join a coaching institute such as Cuemath to give them a better idea of how to deal with problems based on the same. At Cuemath, the certified tutors help kids to build a robust mathematical foundation while ensuring that kids fall in love with the subject and enjoy learning it.

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