Question

Classify the following expression by degree and term:x3y + 5xyz

3rd degree trinomial
4th degree binomial
3rd degree binomial
5th degree binomial

*btw I don't think it's C because it says I got it wrong*

Answer 1

Answer:

Option B is correct

4th degree binomial

Step-by-step explanation:

Binomial means it has two terms.

Degree means the highest exponent on its variables.

Given the expression:

$x^3y+5xyz$

In this expression :

There are two terms i.e, $x^3y , 5xyz$

⇒This expression is a binomial

To determine the degree:

Variables in $x^3y$ , $5xyz$ are a part of same term to determine the degree, we must add their exponents i.e,

In $x^3y$

Degree = 3 +1 = 4

In $5xyz$

Degree = 1+1 +1 = 3

By definition of degree:

Highest exponents is 4

Therefore, the given expression is 4th degree binomial

Answer 2

You can use the fact that a binomial is a two termed polynomial and the degree of a polynomial is highest power of its terms.

The given expression is classified as

Option B: 4th degree binomial

What is a polynomial?

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

Example: $x^3 + 3x + 5$ is a polynomial.

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:  $x^3 + 3x + 5$ is a polynomial consisting 3 terms as $x^3, 3x \: \rm and \: 5$

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

What is degree of a polynomial?

Degree of a polynomial is the highest power that its terms pertain(for multivariables, the power of term is addition of power of variables in that term).

Thus, in  $x^3 + 3x + 5$ , the degree of the polynomial is 3 as the height power in its terms is 3.

(power and exponent are same thing)

Using the above definitions to identify the type of the given expression:

The given polynomial is

$x^3y + 5xyz$

There are two terms, thus, it is binomial

The first term has power 3 + 1 = 4

The second term has power 1 + 1 + 1 = 3 (variables not raised to power mean they're raised with 1 as its power since something raised to 1 power is resulted as that thing itself)

The highest power of the given expression is 4

Thus,

The given expression is classified as

Option B: 4th degree binomial

Learn more about polynomials here:

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