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What else can I help you with?
When adding polynomials what do you do to the exponents?
You keep them the same if they have different bases
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.
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.
The exponents in the terms of a polynomial must be?
why the exponents can not be negative
When multiplying binomials that turn out negative do you add or subtract exponents?
When multiplying numbers with exponents, you add the exponents.
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.
Do all polynomials have exponents?
Yes.
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.
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
When you multiply polynomials what do you do with the exponents?
Add them up providing that the bases are the same.
Polynomials are written with the exponents of the terms in what type of order?
descending form
Is negative integers are polynomials?
No.
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.
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.
Can you have negative exponents in the denominator?
You can have negative exponents anywhere. When they are in the denominator, they are equivalent to positive exponents in the numerator of a fraction.
Can a polynomial have a negative exponent?
Polynomials cannot have negative exponent.
