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Need help for question one in polynomials

Need help for question one in polynomials-example-1

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Answer:

a) monomial
b) constant
c) binomial
d) trinomial
e) binomial
f) constant
g) monomial

Explanation:

Let's start by defining the terms in the question:
A monomial is an expression with a single term, regardless of how many variables are in the term.
A binomial is an expression with two different terms, which cannot be combined into a single term due to their variables not matching.
A trinomial is an expression with three different terms, which cannot be combined into a binomial or monomial because their variables do not match.
A constant is an integer that lacks a variable attached to it. An integer with a variable attached to it would be a monomial, and the integer itself would be called a coefficient.

Now, we can get into the parts of the question:
a) 8a²b is two variables however it is still a single term so this is a monomial.

b) -39 is an integer with no variables attached. Therefore, it is a constant.

c) x + y is two variables and two different terms that cannot be combined into one single term. It is a binomial.

d) -12xy + 5y - x² showcases three different variables and three different terms that cannot be consolidated. Thus, it is a trinomial.

e) 2x² + 2y² demonstrates two different variables and two different terms that are not alike. As such, we have a binomial.

f) 3/4 is an integer with no variables in sight. We have here a constant.

g) -32m²n² has two variables but is only a single term on its own. This is a monomial.

User Bruno Leite
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