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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.
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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
What property is used to multipy a term or terms into a polynomial?
The property used to multiply a term or terms into a polynomial is the Distributive Property. This property states that when you multiply a number (or term) by a sum, you distribute the multiplication across each term within the parentheses. For example, when multiplying (a(b + c)), you would apply the distributive property to get (ab + ac).
Division of Monomials and Polynomials by Monomials?
to multiplya polynomial by a monomial,use the distributive property and then combine like terms.
How do you convert factored to general form?
To convert a polynomial from factored form to general form, you need to expand the factored expression by multiplying the factors together. For example, if you have a factored expression like ( (x - 2)(x + 3) ), you would use the distributive property (also known as the FOIL method for binomials) to multiply: ( x^2 + 3x - 2x - 6 ), which simplifies to ( x^2 + x - 6 ). Continue this process for any additional factors until the expression is fully expanded into its general form, which is typically written as a polynomial in standard form.
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.
How do you convert factored to general form?
To convert a polynomial from factored form to general form, you need to expand the factored expression by multiplying the factors together. For example, if you have a factored expression like ( (x - 2)(x + 3) ), you would use the distributive property (also known as the FOIL method for binomials) to multiply: ( x^2 + 3x - 2x - 6 ), which simplifies to ( x^2 + x - 6 ). Continue this process for any additional factors until the expression is fully expanded into its general form, which is typically written as a polynomial in standard form.
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!
A polynomial that can be factored is called?
It is still called a polynomial.
What two properties are commonly used when multiplying a monomial by a polynomial?
Distributive property of multiplication over addition, Commutativity of addition.
Use the greatest common factor and the distributive property to write equivalent expressions in factored form. 13ab + 15ab?
28ab
A polynomial that can not be factored is called?
If a number cannot be factored it is a prime number.
What is the polynomial when each of its factors is prime?
Completely Factored
