Answer:
The expression is a polynomial.
Trinomial (according to the number of terms)
Step-by-step explanation:
Given the algebraic expression, 6x² + x + 1:
A <u>term</u> comprises of a product of numerical coefficient and one of more variables raised to powers. Like terms have the same variables and exponents.
While a <u>polynomial</u> is a term (or finite sum of terms), comprising of variables with positive or zero integer exponents. Strictly defined, the terms within a polynomial expression <em>cannot</em> include variables as a denominator.
A <u>monomial</u> is a single-termed polynomial.
A <u>binomial</u> is a polynomial with two terms.
A <u>trinomial</u> is a polynomial that has exactly three terms.
With these given definitions, we can infer that the given polynomial expression, 6x² + x + 1, is a trinomial, given that it has three terms:
- 6x² is the leading term with the highest degree or exponent. Specifically, the name of this term is <u><em>quadratic</em></u>, given its exponent of 2.
- x is a <u><em>linear</em></u> term, given its exponent of 1.
- 1 is a <u><em>constant</em></u> term.
Therefore, the given expression is a <u>polynomial</u> containing three terms, making it a <u>trinomial</u>.
