Which of the following statements are true?
There is more than one correct answer choice. Select all correct answer choices.
A)All monomials are polynomials.
B)All polynomials have at least one monomial as a term.
C)All binomials are polynomials.
D)All the terms of a polynomial must be monomials.
E)All polynomials are binomials.
F)All polynomials are monomials.
A, B, C?
correct
thank you!
Yes, A, B, and C are all correct answer choices.
A) All monomials are polynomials. This is true because a monomial is a polynomial with only one term.
B) All polynomials have at least one monomial as a term. This is also true because a polynomial is a sum of terms, and each term can be a monomial.
C) All binomials are polynomials. This is true because a binomial is a polynomial with two terms.
To determine which of the statements are true, let's break down each statement and analyze them:
A) All monomials are polynomials:
This statement is true. A monomial is a polynomial with a single term. So if something is a monomial, it is also a polynomial.
B) All polynomials have at least one monomial as a term:
This statement is true. Since a polynomial is a combination of terms, it must have at least one monomial as one of its terms.
C) All binomials are polynomials:
This statement is true. A binomial is a polynomial with two terms. Therefore, all binomials are indeed polynomials.
D) All the terms of a polynomial must be monomials:
This statement is false. A polynomial can have multiple types of terms, such as monomials, binomials, trinomials, etc. The only requirement is that the terms include variables raised to non-negative integer exponents (whole numbers) and can be combined using addition or subtraction.
E) All polynomials are binomials:
This statement is false. As mentioned earlier, a polynomial can have more than two terms (such as a trinomial or a polynomial with even more terms). So, not all polynomials are binomials.
F) All polynomials are monomials:
This statement is false. As mentioned earlier, a polynomial can have multiple terms, including monomials, binomials, and more. So, not all polynomials are monomials.
Therefore, the correct answer choices are A) All monomials are polynomials, B) All polynomials have at least one monomial as a term, and C) All binomials are polynomials.