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Division of Monomials and Polynomials by Monomials?
to multiplya polynomial by a monomial,use the distributive property and then combine like terms.
Why are polynomials not closed under division?
Polynomials are not closed under division because dividing one polynomial by another can result in a quotient that is not a polynomial. Specifically, when a polynomial is divided by another polynomial of a higher degree, the result can be a rational function, which includes terms with variables in the denominator. For example, dividing (x^2) by (x) gives (x), a polynomial, but dividing (x) by (x^2) results in (\frac{1}{x}), which is not a polynomial. Thus, the closure property does not hold for polynomial division.
Explain how you multiply two polynomials?
To multiply two polynomials, you apply the distributive property, also known as the FOIL method for binomials. Each term in the first polynomial is multiplied by each term in the second polynomial. After performing all the multiplications, you combine like terms to simplify the resulting polynomial. Finally, ensure that the polynomial is written in standard form, with terms ordered by decreasing degree.
What is the distributive property when multiplying polynomials?
You just multiply the term to the polynomials and you combine lije terms
Can you use the Associative Property with subtraction and division?
No you can not use subtraction or division in the associative property.
What property of polynomial subtraction says hat the difference of two polynomials is always a polynomial?
Closure
Which property of polynomial addition says that the sum of two polynomials is always a polynomial?
It is called the property of "closure".
Which property of polynomial multiplication says that the product of two polynomials is always a polynomial?
That property is called CLOSURE.
What property of polynomial multiplication says that the product of two polynomials is always a polynomial?
Clouser
Division of Monomials and Polynomials by Monomials?
to multiplya polynomial by a monomial,use the distributive property and then combine like terms.
Do you use the distributive property with a monomial and a polynomial?
If you want to multiply the monomial by the polynomial, yes. In that case, you have to multiply the monomial by every term of the polynomial. For example: a (b + c + d) = ab + ac + ad More generally, when you multiply together two polynomials, you have to multiply each term in one polynomial by each term of the other polynomial; for example: (a + b)(c + d) = ac + ad + bc + bd All this can be derived from the distributive property (just apply the distributive property repeatedly).
Can multiplication be distributive over subtraction?
Multiplication can be the first step when using the distributive property with subtraction. The distributive law of multiplication over subtraction is that the difference of the subtraction problem and then multiply, or multiply each individual products and then find the difference.
What is the distributive property when multiplying polynomials?
You just multiply the term to the polynomials and you combine lije terms
Can you use the Associative Property with subtraction and division?
No you can not use subtraction or division in the associative property.
Does the communitive property work with subtraction?
yes it does work for subtraction
What property is used to multiply a term into a polynomial?
Distributive Property
Is subtraction an identity property?
Subtraction is not an identity property but it does have an identity property. The identity is 0 and each number is its own inverse with respect to subtraction. However, this is effectively the same as the inverse property of addition so there is no real need to define it as a separate property.
