Respuesta :
Answer:
x2y – 3x, 6y2 – y, -4xy – 2/5 Are the answers
Step-by-step explanation:
i just finished it on edgnuity and it show that is the answer
The algebraic expressions out of the given options that are binomials is given by: Option B: x^2y - 3x and Option D: 4xy - 2/5
What are polynomials?
Polynomials are algebraic expressions having only addition, subtraction, multiplication and exponentiation (non-negative) of variables involved in it.
What are terms in polynomials?
Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Example:
[tex]x^3 + 3x +5[/tex]
is a polynomial consisting 3 terms as
[tex]x^3[/tex], 3x and 5
- If there is one term, the polynomial will be called monomial.
- If there are two terms, the polynomial will be called binomial
- If there are three terms, the polynomial will be called trinomial
Checking all the options:
- Option 1: [tex]xy\sqrt{8}[/tex]
It has only one term, so its not a binomial.
- Option 2: [tex]x^2y - 3x[/tex]
It has two terms, and there is only integer powers of variables and variables are in multiplication in forming terms, so its a polynomial. And because of two terms and being polynomial, it is binomial.
- Option 3: [tex]y^2 + \sqrt{y}[/tex]
Because of square root over variable 'y', the variable 'y' got non-integer power 1/2 as square root is also written as exponentiation by 1/2.
Thus, its not a polynomial.
- Option 4: [tex]4xy - 2/5\\[/tex]
Its a polynomial as there are constants only and variables with multiplication. And because of two terms and being polynomial, it is binomial.
- Option 5: [tex]x^2 + \dfrac{3}{x}[/tex]
we can write the second term as:
[tex]\dfrac{3}{x} = 3x^{-1}[/tex]
Thus, the variable x has negative power. Thus, its not a polynomial. Or simply, since the variable is in division in simplified form, therefore, its not a polynomial.
Thus, the algebraic expressions out of the given options that are binomials is given by: Option B: x^2y - 3x and Option D: 4xy - 2/5
Learn more about binomials here:
https://brainly.com/question/10451213
