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What is the meaning of rational algebraic expression?
A rational algebraic expression is the ratio of two polynomials, each with rational coefficients. By suitable rescaling, both the polynomials can be made to have integer coefficients.
What are the rules in addition of polynomials?
Add together the coefficients of "like" terms. Like terms are those that have the same powers of the variables in the polynomials.
Can polynomials have radicals?
no only the coefficients can. like rad 5 but not x or y
What are 6 myths of polynomials?
Some common myths about polynomials include: All polynomials have real roots: This is false; polynomials can have complex roots as well. The degree of a polynomial dictates its shape: While the degree influences the general behavior, other factors like coefficients also play a significant role. Polynomials must have integer coefficients: Polynomials can have coefficients that are rational, real, or even complex numbers. A polynomial of degree n always has n roots: This is only true in the complex number system; in the real number system, some roots may be complex or repeated.
Rules in adding polynomials?
To add polynomials , simply combine similar terms. Combine similar terms get the sum of the numerical coefficients and affix the same literal coefficient .
What does poloments mean?
"Poloments" appears to be a misspelling. If you meant "polynomials," they are mathematical expressions with multiple terms involving variables and coefficients. Polynomials are commonly used in algebra and calculus.
Will the product of two polynomials always be a polynomial?
Yes, the product of two polynomials will always be a polynomial. This is because when you multiply two polynomials, you are essentially combining like terms and following the rules of polynomial multiplication, which results in a new polynomial with coefficients that are the products of the corresponding terms in the original polynomials. Therefore, the product of two polynomials will always be a polynomial.
What is the definition of cofficient of polynomial?
The coefficients of polynomials are the numbers in front of the variable expressions. Ex: In the polynomial: 3x^5 + 12x^2 - 45x + 134 the numerical coefficients are: 3,12,& -45
How are adding and multiplying polynomials different from each other?
Adding polynomials involves combining like terms by summing their coefficients, resulting in a polynomial of the same degree. In contrast, multiplying polynomials requires applying the distributive property (or FOIL for binomials), which results in a polynomial whose degree is the sum of the degrees of the multiplied polynomials. Essentially, addition preserves the degree of the polynomials, while multiplication can increase it.
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.
What are the arrangement of chips in polynomial damath?
In polynomial damath, chips are arranged in a grid format where each row represents a different polynomial degree, and each column corresponds to the coefficients of these polynomials. Players use chips to represent positive or negative coefficients, typically in a binary format, allowing for a visual and interactive way to perform polynomial addition, subtraction, and multiplication. The arrangement helps players easily manipulate and compute polynomials through strategic placement and movement of chips.
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.
