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The distributive property allows us to simplify expressions by distributing a term across a sum or difference. When factoring a polynomial, we can reverse this process by identifying common factors in each term of the polynomial. For example, in the expression ( ax + ay ), we can factor out ( a ) to get ( a(x + y) ). This reveals the common factor and simplifies the polynomial into a product of its factors.
What else can I help you with?
What property is used to multiply a term into a polynomial?
Distributive Property
What property is used when finding the product of a monomial and a polynomial?
Distributive
Division of Monomials and Polynomials by Monomials?
to multiplya polynomial by a monomial,use the distributive property and then combine like terms.
What is the value of having factored form of a polynomial?
The factored form of a polynomial is valuable because it simplifies the process of finding its roots or zeros, making it easier to solve equations. It also provides insights into the polynomial's behavior, such as identifying multiplicities of roots and understanding its graph. Additionally, factored form can facilitate polynomial division and help in applications such as optimization and modeling in various fields.
Why can't a polynomial be factored?
It can, so the question does not make sense.
What property is used to multiply a term into a polynomial?
Distributive Property
What property is used when finding the product of a monomial and a polynomial?
Distributive
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).
How do you know if a polynomial is in factored form?
You can't know if a general polynomial is in factored form.
Division of Monomials and Polynomials by Monomials?
to multiplya polynomial by a monomial,use the distributive property and then combine like terms.
A polynomial that can be factored is called?
It is still called a polynomial.
What is a simplified polynomial?
a simplified polynomial is a algebraic equation/expression with variables and constants that can can be written as a sum of terms. Simplified form is the opposite of factored form P(x) = ( 2x - 3)( x+4 ) Is a factored form - product of 2 factors. Simplify P(x) by using the distributive property: P(x) = 2x2 +8x - 3x -12 P(x) = 2x2 + 5x - 12 simplified : a sum of terms!
What two properties are commonly used when multiplying a monomial by a polynomial?
Distributive property of multiplication over addition, Commutativity of addition.
A polynomial that can not be factored is called?
If a number cannot be factored it is a prime number.
Use the greatest common factor and the distributive property to write equivalent expressions in factored form. 13ab + 15ab?
28ab
What is the polynomial when each of its factors is prime?
Completely Factored
What is the distributive property for 46 and 69?
The distributive property is a characteristic that two mathematical operators may have. Numbers do not have a distributive property.
