0
Want this question answered?
Be notified when an answer is posted
Add your answer:
Earn +20 pts
What is the meaning degree of polynomial?
The degree of a polynomial is the highest exponent on any independent variable in the polynomial.
How many terms does the polynomial have?
As many as you like. A polynomial in 1 variable, and of degree n, can have n+1 terms where n is any positive integer.
What is meant by the degree of a monomial and polynomial?
The degree is the highest power of the variable that appears in it.(x2 + x + 9) is a second degree polynomial(Q4 - 72) is a fourth degree polynomial( z ) is a first degree monomialSo the degree of a polynomial in one variable is the highest power of the variable.For example, [ 2x3 - 7x ] has degree 3.The degree of a polynomial in two or more variables is the greatest sum of theexponents in any single term.For example, [ 5m3 + m2n - mn2 ] has degree 4.And a degree of a monomial is the sum of the exponents of its variables.For example, [ 4a2b3 ] has degree 5.
Is every monomial a polynomial?
Yes. A monomial is a zero-degree polynomial. Although the prefix poly means "several" the definition allows for any finite number of terms.
How do you identify the polynomials of degree one?
The degree of a polynomial is determined by the highest degree of the terms within it, and the degree of the terms is determined by the power of the variable and the amount of variables in it.For example, the term 3x has a degree of one, as does 5y. However when there is more than one variable you add the degrees together, so 4xy has a degree of 2, not 1. Any single variable to the 2nd power e.g. 8x2 also has a degree of 2.So a polynomial of one degree is a polynomial where each of its terms only have one variable to the first power so 5+x is to one degree, as is 1+2x+3y+4z despite having more than one variable in the expression.
What is the meaning degree of polynomial?
The degree of a polynomial is the highest exponent on any independent variable in the polynomial.
How many terms does the polynomial have?
As many as you like. A polynomial in 1 variable, and of degree n, can have n+1 terms where n is any positive integer.
What is meant by the degree of a monomial and polynomial?
The degree is the highest power of the variable that appears in it.(x2 + x + 9) is a second degree polynomial(Q4 - 72) is a fourth degree polynomial( z ) is a first degree monomialSo the degree of a polynomial in one variable is the highest power of the variable.For example, [ 2x3 - 7x ] has degree 3.The degree of a polynomial in two or more variables is the greatest sum of theexponents in any single term.For example, [ 5m3 + m2n - mn2 ] has degree 4.And a degree of a monomial is the sum of the exponents of its variables.For example, [ 4a2b3 ] has degree 5.
What is the polynomial of degree 0?
A polynomial of degree 0 is a polynomial without any variables, such as 9.
What is the difference between a polynomial and a quadratic equation?
A quadratic equation is of degree 2, that is, the highest power is 2. A polynomial is not an equation, however, you can convert it into an equation by setting the polynomial equal to zero for example. A polynomial EQUATION can be of any degree: 1, 2, 3, 4, etc.
Is every monomial a polynomial?
Yes. A monomial is a zero-degree polynomial. Although the prefix poly means "several" the definition allows for any finite number of terms.
How do you identify the polynomials of degree one?
The degree of a polynomial is determined by the highest degree of the terms within it, and the degree of the terms is determined by the power of the variable and the amount of variables in it.For example, the term 3x has a degree of one, as does 5y. However when there is more than one variable you add the degrees together, so 4xy has a degree of 2, not 1. Any single variable to the 2nd power e.g. 8x2 also has a degree of 2.So a polynomial of one degree is a polynomial where each of its terms only have one variable to the first power so 5+x is to one degree, as is 1+2x+3y+4z despite having more than one variable in the expression.
What is the number in front of the term with the highest degree in a polynomial?
It is the Coefficient. It only refers to the given term that it is front. e.g. 2x^2 - 3x + 1 The '2' in front of 'x^2' only refers to 'x^2'. The '-3' in front of 'x' is the coefficient of '-3' The '1' is a constant.
What is the degree of the polynomial root 2?
If there aren't any variables, the degree is zero.
What is a polynomial that doesn't have any like terms?
zero polynomial which is 0 and only 0 = 0.
What are the steps to solve these problems Find the degree of each polynomial 5a-2b2 plus 1 and 24xy-xy3 plus x2?
The degree of a polynomial function is the highest power any single term is raised to. For example, (5a - 2b^2) is a second degree function because the "b^2" is raised to the second power and the "a" is only raised to the (implied) first power. For (24xy-xy^3 + x^2) it is a third degree polynomial because the highest power is the cube of -xy.
How do you name polynomials?
There are 2 ways to name a polynomial: by its degree (the highest power) and by the number of terms it has. Some of the most common names based on degree are: constant (meaning there is no variable--5 or 23, for instance; you could also realize that the variable is being raised to the 0 power), linear (the variable is raised to the first power--3x), quadratic (x2), cubic (x3), quartic (x4), and quintic (x5). Keep in mind that these terms could have any coefficients and any number of terms, just be sure you name it based on the highest power (ex: 3x4 + 5x3 - 2x is a quartic polynomial, whereas 3x4 + 5x3 - 2x5 would be a quintic polynomial). To name a polynomial based on the number of terms, make sure you've simplified it by combining all like terms, then count them up. If the polynomial has: 1 term--monomial (mono- means 1; like a monorail) 2 terms--binomial (bi- means 2; like a bicycle) 3 terms--trinomial (tri- means 3; like a triangle) 4 or more terms--just call it a polynomial, unless your teacher gives you more names (poly- means many; like a polygon). Keep in mind that these terms will often be used together: 3x4 + 5x3 - 2x is a quartic trinomial. (You may be thinking that I was wrong above where I called this same example a quartic polynomial--that was also correct, since monomial, binomial, and trinomial are all just more specific names for a polynomial)
