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What does it mean for a polynomial to be closed under addition subtraction and multiplication?
It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.
What is the definition of non polynomial?
Actually, it is easier to define a polynomial as a function of a variable, x, in the form:p(x) = anxn + an-1xn-1 + ... + a2x2 + a1x + a0 where n is an integer and the ai are constants. A non-polynomial, then, is any function of x which contains one or more terms in x which are not in the form akxk.
How do you find the leading term of a polynomial?
If the polynomial is in terms of the variable x, then look for the term with the biggest power (the suffix after the x) of x. That term is the leading term. So the leading term of x2 + 5 + 4x + 3x6 + 2x3 is 3x6 If you are likely to do any further work with the polynomial, it would be a good idea to arrange it in order of the descending powers of x anyway.
A value of a polynomial is a value for which the polynomial is bigger or smaller than any other nearby values?
extreme
What is the difference between a polynomial and a quadratic equation?
Oh, dude, it's like this: all quadratic equations are polynomials, but not all polynomials are quadratic equations. A quadratic equation is a specific type of polynomial that has a degree of 2, meaning it has a highest power of x^2. So, like, all squares are rectangles, but not all rectangles are squares, you know what I mean?
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.
If a polynomial is the difference of two squares?
No, a polynomial is the sum of any two monomials, i.e., any two terms, for example, a + b, a - b, a2 + b2, x2y -3, etc. ("Sum" may include negative terms.)No, a polynomial is the sum of any two monomials, i.e., any two terms, for example, a + b, a - b, a2 + b2, x2y -3, etc. ("Sum" may include negative terms.)No, a polynomial is the sum of any two monomials, i.e., any two terms, for example, a + b, a - b, a2 + b2, x2y -3, etc. ("Sum" may include negative terms.)No, a polynomial is the sum of any two monomials, i.e., any two terms, for example, a + b, a - b, a2 + b2, x2y -3, etc. ("Sum" may include negative terms.)
How can you determine that an algebraicexpresion not a polynomial?
If all of its terms are of the form ax^b where a is any constant and b is a non-negative integer then it is a polynomial. If not, it is not.
Are polynomial and mononomial the same?
No. A monomial (watch the spelling, please - only one "no") is a special case of a polynomial. A polynomial may have any number of terms; a monomial has exactly one term.
What does associate property mean in math?
When the terms in a polynomial are commutative, they can be grouped with parentheses in any way.
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)
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.
What do you call a polynomial that has 5 terms?
quatric i think :D Because it doesn't go any higher than it does after four terms Hope this helped
What number can you add to x2-10x to a polynomial?
-8
What is the polynomial of degree 0?
A polynomial of degree 0 is a polynomial without any variables, such as 9.
What is the meaning degree of polynomial?
The degree of a polynomial is the highest exponent on any independent variable in the polynomial.
What are the roots of polynomial?
The "roots" of a polynomial are the solutions of the equation polynomial = 0. That is, any value which you can replace for "x", to make the polynomial equal to zero.
