Monomials - Basics and Properties

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What is a monomial?
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A monomial is an algebraic expression consisting of one term, which can include numbers, variables, or their products.
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Can a single number be considered a monomial?
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Yes, a single number, also known as a constant, is considered a monomial.
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What is the degree of a monomial?
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The degree of a monomial is the sum of the exponents of all its variables.
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Is 7x^3y a monomial?
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Yes, 7x^3y is a monomial because it is a single algebraic term combining a constant and variables.
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What operation cannot be part of a monomial?
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A monomial cannot include addition or subtraction operations.
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Can a monomial have a negative exponent?
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No, a monomial does not contain negative exponents according to standard definition.
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How do you multiply monomials?
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To multiply monomials, multiply the coefficients and add the exponents of like variables.
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What is an example of a monomial in one variable?
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An example is 4x^5, which is a monomial consisting of a number and a single variable with an exponent.
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Can a monomial contain a fraction?
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Yes, a monomial can include fractions as coefficients as long as it has only one term.
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How do you find the greatest common factor (GCF) of two monomials?
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To find the GCF, take the lowest power of all common variables and the greatest common divisor of coefficients.
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What is the GCF of 12x^3 and 8x^2?
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The GCF is 4x^2.
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How do monomials differ from polynomials?
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Monomials consist of one term, while polynomials have two or more terms.
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What happens when you raise a monomial to a power?
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Raise the coefficient to the power and multiply each exponent by the power.
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Is x^-3 a monomial?
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No, x^-3 is not a monomial in standard form since it has a negative exponent.
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What is the coefficient in the monomial 5xy^2?
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The coefficient is 5.
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