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What else can I help you with?
Polynomials have factors that are?
Other polynomials of the same, or lower, order.
What are polynomials that have factors called?
Reducible polynomials.
When can you say that the term is a term of polynomials?
If a term consists of one or more of: a numerical coefficientnon-negative integer exponents of variable(s),then it is a term of a polynomial. If a term consists of one or more of: a numerical coefficientnon-negative integer exponents of variable(s),then it is a term of a polynomial. If a term consists of one or more of: a numerical coefficientnon-negative integer exponents of variable(s),then it is a term of a polynomial. If a term consists of one or more of: a numerical coefficientnon-negative integer exponents of variable(s),then it is a term of a polynomial.
Which of the expressions are not polynomials?
Exponential, trigonometric, algebraic fractions, inverse etc are all examples.
Trinomial are polynomials?
Yes.
Polynomials are written with the exponents of the terms in order?
descending
When adding polynomials what do you do to the exponents?
You keep them the same if they have different bases
Polynomials are written with the exponents of the terms in what type of order?
descending form
When you multiply polynomials what do you do with the exponents?
Add them up providing that the bases are the same.
Why do you think the definition for polynomials is so restrictive?
The definition for polynomials is very restrictive. This is because it will give more information. It excludes radicals, negative exponents, and fractional exponents. When these are included, the expression becomes rational and not polynomial.
Is monomials are polynomials?
Yes, monomials are a specific type of polynomial. A monomial is a polynomial that consists of only one term, which can include variables raised to non-negative integer exponents and coefficients. In contrast, a polynomial can have multiple terms, such as binomials (two terms) or trinomials (three terms). Therefore, all monomials are polynomials, but not all polynomials are monomials.
When you add polynomials what do you do with your exponents?
Nothing. The exponents are not affected when added polynomials. However, they play a role in which variables add or subtract another variable. For example. (3x^2+5x-6)+(4x^2-3x+4) The exponents would determine that when adding these polynomials that 3x^2 would be added to 4x^2 and so forth 5x-3x and finally -6 would be added to 4. With a final conclusion of (7x^2+2x-2)
Are polynomials a closed set under addition?
Yes, polynomials are a closed set under addition. This means that if you take any two polynomials and add them together, the result will also be a polynomial. The sum of two polynomials retains the structure of a polynomial, as it still consists of terms with non-negative integer exponents and real (or complex) coefficients.
How do you make working model of maths on polynomials?
Polynomials are the simplest class of mathematical expressions. The expression is constructed from variables and constants, using only the operations of addition, subtraction, multiplication and non-negative integer exponents.
What is the answer called when 2 or more polynomials are multipiled?
A polynomial is any number of the form Ax^n + Bx^n-1 + ... + c. So, multiplying numbers with exponents with any other numbers with exponents in polynomials only results in another, larger polynomial. Since this is multiplication, you could call the resultant polynomial a product.
Is every algebraic expression is a polynomial?
Not every algebraic expression is a polynomial. A polynomial consists of terms that are non-negative integer powers of variables, combined using addition, subtraction, and multiplication. In contrast, algebraic expressions can include terms with negative or fractional exponents, such as (x^{-1}) or (x^{1/2}), which do not qualify as polynomials. Therefore, while all polynomials are algebraic expressions, not all algebraic expressions are polynomials.
What is alike of polynomials and nonpolynomial?
Polynomials and nonpolynomial expressions both represent mathematical functions and can be used to model relationships between variables. They share the property of being defined over real or complex numbers, and both can appear in equations and inequalities. However, polynomials consist solely of non-negative integer exponents on their variables, while nonpolynomials may include variables raised to fractional or negative exponents, transcendental functions, or other forms that do not fit the polynomial criteria.
