Concept explainers
Determine whether the following algebraic expression is a polynomial. Answer Yes or No. If it is a polynomial, state the degree and then state whether it is a monomial, a binomial, or a trinomial: 6x2y4 − 8x5 + 3.
Whether the expression 6x2y4−8x5+3 is a polynomial or not and find the degree.
Answer to Problem 1PCT
Yes, the given expression is a trinomial of degree 6.
Explanation of Solution
Definition used:
“A monomial or sum of monomials is known as a polynomial. The degree of a polynomial is the largest degree of all the terms in that polynomial”.
Observation:
The given expression is 6x2y4−8x5+3.
Observe that each term is either a number, a product of a number and a variable, a product of two variables or a variable alone, where all exponents are non-negative numbers.
Thus, the given expression is a sum of three monomials.
Hence, the given expression is a polynomial.
The degrees of the terms in the expression are as follows, {6, 5, 0}. The maximum of the degrees is 6.
Thus, the degree of the given polynomial is 6.
Thus, the given expression is a trinomial with degree 6.
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