Question

Explain in words how you would classify the following polynomial

y + yx³ - x³ + 2x³
A) Trinomial
B) Binomial
C) Quadrinomial
D) Monomial

Answer 1

The polynomial
`\( y + yx^3 - x^3 + 2x^3 \)` is classified as a Quadrinomial. Thus the correct option is (C).

Step-by-step explanation:

Polynomials are algebraic expressions comprising variables and coefficients, involving addition, subtraction, multiplication, and non-negative integer exponents. In this particular polynomial, there are four distinct terms, each containing a combination of variables and coefficients. The presence of four terms categorizes it as a quadrinomial.

Now, let's break down the given polynomial for a more comprehensive understanding. The terms are y,
`\(yx^3\)`,
`\(-x^3\)`, and
`\(2x^3\)`. Notice that the exponents on the variable x vary across the terms, with
`\(x^3\)` being the highest power. This indicates a degree of 3 for the polynomial. The coefficient 2 in the last term,
`\(2x^3\)`, contributes to the overall count of terms.

The classification as a quadrinomial is derived from the sum of terms, with each term representing a distinct monomial. Specifically, the polynomial consists of four monomials: y,
`\(yx^3\)`,
`\(-x^3\), and \(2x^3\)`. Therefore, the appropriate classification is a quadrinomial, aligning with the standard naming conventions for polynomials based on the number of terms they encompass.