Monomials - Basics and Properties

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What is a monomial?

A monomial is an algebraic expression consisting of one term, which can include numbers, variables, or their products.

Can a single number be considered a monomial?

Yes, a single number, also known as a constant, is considered a monomial.

What is the degree of a monomial?

The degree of a monomial is the sum of the exponents of all its variables.

Is 7x^3y a monomial?

Yes, 7x^3y is a monomial because it is a single algebraic term combining a constant and variables.

What operation cannot be part of a monomial?

A monomial cannot include addition or subtraction operations.

Can a monomial have a negative exponent?

No, a monomial does not contain negative exponents according to standard definition.

How do you multiply monomials?

To multiply monomials, multiply the coefficients and add the exponents of like variables.

What is an example of a monomial in one variable?

An example is 4x^5, which is a monomial consisting of a number and a single variable with an exponent.

Can a monomial contain a fraction?

Yes, a monomial can include fractions as coefficients as long as it has only one term.

How do you find the greatest common factor (GCF) of two monomials?

To find the GCF, take the lowest power of all common variables and the greatest common divisor of coefficients.

What is the GCF of 12x^3 and 8x^2?

The GCF is 4x^2.

How do monomials differ from polynomials?

Monomials consist of one term, while polynomials have two or more terms.

What happens when you raise a monomial to a power?

Raise the coefficient to the power and multiply each exponent by the power.

Is x^-3 a monomial?

No, x^-3 is not a monomial in standard form since it has a negative exponent.

What is the coefficient in the monomial 5xy^2?

The coefficient is 5.


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1. What is a monomial?

A polynomial with two or more terms.

An algebraic expression involving addition or subtraction.

A monomial is an algebraic expression consisting of one term, which can include numbers, variables, or their products.

An equation that always equals zero.

2. Can a single number be considered a monomial?

No, a single number cannot be a monomial.

Yes, a single number, also known as a constant, is considered a monomial.

Only if it's a positive integer.

Only if it's part of a fraction.

3. What is the degree of a monomial?

The number of different variables in the monomial.

The degree of a monomial is the sum of the exponents of all its variables.

The coefficient of the term.

The highest power of any variable.

4. Is 7x^3y a monomial?

Yes, 7x^3y is a monomial because it is a single algebraic term combining a constant and variables.

No, it contains both variables and constants.

Yes, but only if y is zero.

No, it contains too many variables.

5. What operation cannot be part of a monomial?

A monomial cannot include addition or subtraction operations.

Multiplication can never be part of a monomial.

Exponentiation is not allowed in a monomial.

Division cannot be involved in a monomial.

6. Can a monomial have a negative exponent?

Yes, negative exponents are allowed in monomials.

No, a monomial does not contain negative exponents according to standard definition.

Yes, but only if the coefficient is positive.

It depends on the number of variables.

7. How do you multiply monomials?

By adding the coefficients only.

By subtracting the exponents of like variables.

To multiply monomials, multiply the coefficients and add the exponents of like variables.

Multiply both the coefficients and the exponents separately.

8. What is an example of a monomial in one variable?

An example is 4x^5, which is a monomial consisting of a number and a single variable with an exponent.

2xy^3, since it only has a single term.

3x + 2, as it involves linear operations.

4/x, a single fraction term.

9. Can a monomial contain a fraction?

Yes, a monomial can include fractions as coefficients as long as it has only one term.

No, fractions indicate more than one term.

Only if the numerator and denominator are variables.

Yes, but only if they are whole numbers.

10. How do you find the greatest common factor (GCF) of two monomials?

To find the GCF, take the lowest power of all common variables and the greatest common divisor of coefficients.

Add the coefficients and compare variable degrees.

Multiply the coefficients and subtract exponent powers.

Subtract the variables and add coefficients.

11. What is the GCF of 12x^3 and 8x^2?

8x^3

16x^5

The GCF is 4x^2.

2x

12. How do monomials differ from polynomials?

Monomials consist of one term, while polynomials have two or more terms.

They both consist of only one term, but monomials have coefficients.

Polynomials do not include constants while monomials do.

Monomials are an old term for what is now called polynomials.

13. What happens when you raise a monomial to a power?

It remains unchanged regardless of the power.

Raise the coefficient to the power and multiply each exponent by the power.

Only the variables are affected, coefficients stay the same.

The monomial is converted into a polynomial.

14. Is x^-3 a monomial?

Yes, because it includes only one term.

No, x^-3 is not a monomial in standard form since it has a negative exponent.

Yes, but only in advanced mathematics.

It's considered a polynomial term.

15. What is the coefficient in the monomial 5xy^2?

The coefficient is xy^2.

The coefficient is 5.

The coefficient is full of variables.

The coefficient is 2.