Name of Polynomial (degree): Polynomial of degree 6
5.)
Number of terms: 2
Name of Polynomial (terms): Binomial
Degree: 3
Name of Polynomial (degree): Cubic
Step-by-step explanation:
CLASSIFICATION OF POLYNOMIALS
A polynomial is an expression made up of variables and constants in which the exponents of the variables are only positive integers, not fractions, according to algebra. The addition and subtraction operators are used to separate the polynomial terms. Polynomials are used in the creation of polynomial equations and the definition of polynomial functions.
Polynomials are expressions with a non-zero coefficient in one or more terms. Variables, exponents, and constants are among the terms. The leading term refers to the polynomial's initial term. The first term in a standard polynomial has the highest degree, and the subsequent terms are placed in descending order of the variables' powers or exponents, followed by constant values. The coefficient is the result of multiplying a number by a variable. A constant is a number that does not have any variables.
CLASSIFYING POLYNOMIALS ACCORDING TO DEGREE:
The degree of the polynomial is the power of the leading term or the highest power of the variable. This is accomplished by placing the polynomial terms in ascending order of power. They can be categorized into the following categories based on the degree of the polynomial:
Polynomial with degree 0: constant
Polynomial with degree 1: linear
Polynomial with degree 2: quadratic
Polynomial with degree 3: cubic
Polynomial with degree 4: quartic
Polynomial with degree 5: quintic
Polynomial degree greater than Degree can be named “Polynomial of degree…”
CLASSIFYING POLYNOMIALS ACCORDING TO THE NUMBER OF TERMS:
Polynomials are classified according to the number of terms they contain. There are polynomials with one, two, three, and even more terms. Polynomials are classed as follows based on the number of terms:
Monomial: It refers to a polynomial having only one term. A number or a number and a variable product.
Example: -2x, 5y,
Binomial: It is a polynomial with two terms. These two monomials are connected by + or -.
Example: x + 3,
Trinomial: A polynomial with three terms. Three monomials are connected by + or -.
Example:
Constant: The polynomial containing only the constant term is a constant polynomial.
Example: 8, -29
Polynomial: If the expression contains more than three terms, then the expression is called a Polynomial. More than three monomials connected by + or -.
Example:
APPLICATION:
1.) x + 1
Number of terms: 2
Name of Polynomial (terms): Binomial
Degree: 1
Name of Polynomial (degree): Linear
2.)
Number of terms: 4
Name of Polynomial (terms): Polynomial
Degree: 4
Name of Polynomial (degree): Quartic
3.)
Number of terms: 1
Name of Polynomial (terms): Monomial
Degree: 3
Name of Polynomial (degree): Cubic
4.)
Number of terms: 3
Name of Polynomial (terms): Trinomial
Degree: 6
Name of Polynomial (degree): Polynomial of degree 6
Answers & Comments
Verified answer
Answer:
1.) x + 1
Number of terms: 2
Name of Polynomial (terms): Binomial
Degree: 1
Name of Polynomial (degree): Linear
2.)![2x^{4} +3x^{2} +4x+1 2x^{4} +3x^{2} +4x+1](https://tex.z-dn.net/?f=2x%5E%7B4%7D%20%2B3x%5E%7B2%7D%20%2B4x%2B1)
Number of terms: 4
Name of Polynomial (terms): Polynomial
Degree: 4
Name of Polynomial (degree): Quartic
3.)![-5x^{3} -5x^{3}](https://tex.z-dn.net/?f=-5x%5E%7B3%7D)
Number of terms: 1
Name of Polynomial (terms): Monomial
Degree: 3
Name of Polynomial (degree): Cubic
4.)![x^{6} -3x^{3} +1 x^{6} -3x^{3} +1](https://tex.z-dn.net/?f=x%5E%7B6%7D%20-3x%5E%7B3%7D%20%2B1)
Number of terms: 3
Name of Polynomial (terms): Trinomial
Degree: 6
Name of Polynomial (degree): Polynomial of degree 6
5.)![3x^{3} +2x 3x^{3} +2x](https://tex.z-dn.net/?f=3x%5E%7B3%7D%20%2B2x)
Number of terms: 2
Name of Polynomial (terms): Binomial
Degree: 3
Name of Polynomial (degree): Cubic
Step-by-step explanation:
CLASSIFICATION OF POLYNOMIALS
CLASSIFYING POLYNOMIALS ACCORDING TO DEGREE:
The degree of the polynomial is the power of the leading term or the highest power of the variable. This is accomplished by placing the polynomial terms in ascending order of power. They can be categorized into the following categories based on the degree of the polynomial:
CLASSIFYING POLYNOMIALS ACCORDING TO THE NUMBER OF TERMS:
Polynomials are classified according to the number of terms they contain. There are polynomials with one, two, three, and even more terms. Polynomials are classed as follows based on the number of terms:
Example: -2x, 5y,![6x^{2} 6x^{2}](https://tex.z-dn.net/?f=6x%5E%7B2%7D)
Example: x + 3,
Example:
Example: 8, -29
Example:
APPLICATION:
1.) x + 1
Number of terms: 2
Name of Polynomial (terms): Binomial
Degree: 1
Name of Polynomial (degree): Linear
2.)![2x^{4} +3x^{2} +4x+1 2x^{4} +3x^{2} +4x+1](https://tex.z-dn.net/?f=2x%5E%7B4%7D%20%2B3x%5E%7B2%7D%20%2B4x%2B1)
Number of terms: 4
Name of Polynomial (terms): Polynomial
Degree: 4
Name of Polynomial (degree): Quartic
3.)![-5x^{3} -5x^{3}](https://tex.z-dn.net/?f=-5x%5E%7B3%7D)
Number of terms: 1
Name of Polynomial (terms): Monomial
Degree: 3
Name of Polynomial (degree): Cubic
4.)![x^{6} -3x^{3} +1 x^{6} -3x^{3} +1](https://tex.z-dn.net/?f=x%5E%7B6%7D%20-3x%5E%7B3%7D%20%2B1)
Number of terms: 3
Name of Polynomial (terms): Trinomial
Degree: 6
Name of Polynomial (degree): Polynomial of degree 6
5.)![3x^{3} +2x 3x^{3} +2x](https://tex.z-dn.net/?f=3x%5E%7B3%7D%20%2B2x)
Number of terms: 2
Name of Polynomial (terms): Binomial
Degree: 3
Name of Polynomial (degree): Cubic
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