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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).
Is 2 N an monomial?
yes, 2N is, but not N+2 From WIKIPEDIA: "The first meaning is a product of powers of variables, or formally any value obtained from 1 by finitely many multiplications by a variable. If only a single variable x is considered this means that any monomial is either 1 or a power xn of x, with n a positive integer. If several variables are considered, say, x, y, z, then each can be given an exponent, so that any monomial is of the form xaybzc with a,b,c nonnegative integers (taking note that any exponent 0 makes the corresponding factor equal to 1). The second meaning of monomial includes monomials in the first sense, but also allows multiplication by any constant, so that − 7x5 and (3 − 4i)x4yz13 are also considered to be monomials (the second example assuming polynomials in x, y, z over the complex numbers are considered)."
Classify the following polynomial -32xyz?
Since no terms are added, it is a monomial (one term). Adding the powers of the variables (three variables, each to the first power), you see that it is of degree 3.
Sum of monomials?
A single-term algebraic expression is called a monomial. A monomial is the product of real numbers and variables with nonnegative exponents.How to recognize a monomial?Examples: -2abc; 3/x; -r^2s; 3/4x; xy^-3-2abc and -r^2s are monomials3/x, 3/4x, and xy^-3 are not monomials because each has an unknown variable in the denominator (xy^-3 = x/y^3).The number in front of the variable, or numerical factor, is called the numerical coefficient of the term, or simply coefficient.Examples:2x^2, the coefficient is 2;x^5, the coefficient is 1;-3y, the coefficient is -3;-6a/7, the coefficient is -6/7.Terms that have the same variable factors are like terms. Monomials with the same like terms can be combined. For example,2x + 3x = (2 + 3)x = 5x5x^2y^3 - 2x^2y^3 = (5 - 2)x^2y^3 = 3x^2y^3But 8xy and x cannot be combined because one monomial has x and y as its variables and the second monomial has only x. Therefore, the monomials are not like terms, and the resulting expression will remain 8xy +y.
Factor the trinomial below Enter each factor as a polynomial in descending order?
(x+8)(x-5)
Factor each monomial 10a4?
2•5•a•a•a•a
What are the steps in finding the common monomial factor?
It is similar to finding the greatest common factor only you may have variables involved, so you may factor a constant and variable(s) which all terms are divisible by, for example: The common monomial factor in the following: 5x^2+5x would be 5x because both terms are divisible by 5 and x. 5x (x+1). Just find the constant and variable all terms are divisible by and then the product of those is your common monomial factor.
How do we divide a binomial by a monomial?
You divide each term of the binomial by the monomial, and add everything up. This also works for the division of any polynomial by a monomial.
How do you multiply monomial by a polynomial?
you foil it out.... for example take the first number or variable of the monomial and multiply it by everything in the polynomial...
Factors common to each monomial are called what?
Common factors
What is sqare of a-b?
(a-b)2 = (a-b)(a-b). You have to multiply each term in the left monomial by each term in the right monomial: a2 - ab - ab + b2 = a2 - 2ab + b2.
How do obtain the product of monomial ang binomial?
Multiply each term of the binomial by the monomial. Be particularly careful with signs: (+ times +) or (- times -) equals plus or Like signs = + (+ times -) or (- times +) equals minus or Unlike signs = -
Find the GCF of each pair of monomial of -8x³ and 10a²b²?
To find the GCF of each pair of monomial of -8x³ and 10a²b², we can use the following steps: Write the complete factorization of each monomial, including the constants and the variables with their exponents. -8x³ = -1 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ x ⋅ x ⋅ x 10a²b² = 2 ⋅ 5 ⋅ a ⋅ a ⋅ b ⋅ b Identify the common factors in both monomials. These are the factors that appear in both factorizations with the same or lower exponent. The common factors are: 2 Multiply the common factors to get the GCF. GCF = 2 Therefore, the GCF of each pair of monomial of -8x³ and 10a²b² is 2.
Find the GCF of each pair of monomial of 10a and lza²b?
To find the GCF of each pair of monomials of 10a and lza²b, we can use the following steps: Write the complete factorization of each monomial, including the constants and the variables with their exponents. 10a = 2 ⋅ 5 ⋅ a lza²b = lz ⋅ a ⋅ a ⋅ b Identify the common factors in both monomials. These are the factors that appear in both factorizations with the same or lower exponent. The common factors are : a Multiply the common factors to get the GCF. GCF = a Therefore, the GCF of each pair of monomial of 10a and lza²b = a
What is the greates common monomial factor of 8x3y2 24x2y3 40x2y2?
When you simplify each of those expressions you get 120xy, 210xy and 216xy. The GCF of those is 6xy because it divides evenly into all of them.
What is the definition of a degree of a monomial?
A degree of a monomial is simply what exponent or power the monomial is raised to. Key: ^ means "raised to the power of" -5t^2 means the degree is 2, the number is -5, and the variable which is being put to the power of, is t. the degree has a little trick, however. If there are three monomials or more, being added or subtracted, to make a polynomial, and each has a degree (lone variable has a degree of 1) and the monomial that has the highest degree represnts the whole polynomial's degree.
Is a binomial and monomial equal to a trinomial always sometimes or never?
Mathematically, the question is as solid as smoke. The problem is: What does "and" mean ? Without a mathematical operation specified, we don't know how the binomial and monomial may affect each other, or what the result may be. Having a binomial "and" a monomial, all we have so far is two algebraic expressions written down on our paper. They're not equal to anything except a binomial 'and' a monomial, until we get some clear instructions on how they're supposed to be manipulated.
