Understanding Algebraic Concepts

What is a constant? Provide an example.

• The number e (approximately 2.71) is a variable.

• A constant is a changing value like temperature.

• An example of a constant is the number pi (π), which is approximately 3.14.

• The speed of light is a variable that can change.

Define a variable and give an example.

• y = 10.5

• x = 'hello'

• z = true

• Example of a variable: x = 5

What is an expression? Provide an example.

• An expression is a combination of elements that evaluates to a value. Example: '3 + 5'.

• An expression is a statement that cannot be evaluated. Example: 'Hello World'.

• An expression is a single number. Example: '7'.

• An expression is a type of variable. Example: 'x = 10'.

Explain what a term is in algebra.

• A term in algebra is a single mathematical expression that can include numbers, variables, or both, multiplied together.

• A term in algebra is a graphical representation of a mathematical function.

• A term in algebra is a collection of unrelated numbers and letters.

• A term in algebra is a complete equation that includes an equal sign.

What is a monomial? Give an example.

• x^3 - 4x

• 5xy + 2y^2

• 3x^2

• 2x + 3

Define a binomial and provide an example.

• x^2 - 4

• 5 - 2x + 7y

• 2x + 3y

• 3x + 5

What is a trinomial? Give an example.

• A trinomial is a polynomial with four terms, such as 3x^3 + 2x^2 + x + 1.

• A trinomial is a single term expression, like 5x.

• An example of a trinomial is 2x^2 + 3x + 5.

• An example of a trinomial is x + 4.

Explain what a polynomial is.

• A polynomial is an expression of the form a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are coefficients and n is a non-negative integer.

• A polynomial is a constant value that does not change.

• A polynomial is an equation that can only have one variable.

• A polynomial is a type of function that only includes trigonometric terms.

What are coefficients in a polynomial?

• Coefficients are the numerical values in front of the variable terms in a polynomial.

• Coefficients are the constant terms in a polynomial.

• Coefficients are the variables in a polynomial.

• Coefficients are the powers of the variable terms in a polynomial.

Define factors in the context of algebra.

• Factors are numbers or expressions that multiply together to yield another number or expression.

• Factors are unrelated to multiplication.

• Factors are the results of division only.

• Factors are always prime numbers.