Answer:
Final answer:
Polynomials are classified based on the highest degree of their terms after combining like terms: X³ − 2x is cubic, x³ + 4x² − 6x − 8x² + 6x − 6 simplifies to a quadratic after like terms are combined, 6x + 5 is linear, and 4x² − 4x² + 5 simplifies to a constant polynomial.
Explanation:
To classify each polynomial, we must first simplify the expression by combining like terms. Let's review each term in turn.
X³ − 2x is a cubic polynomial because the highest degree of the variable x is 3.
x³ + 4x² − 6x − 8x² + 6x − 6 simplifies to x³ − 4x², which is a quadratic polynomial even though it has a term with degree 3, because the coefficient of the x³ term is zero after combining like terms.
6x + 5 is a linear polynomial because the highest degree of the variable x is 1.
4x² − 4x² + 5 simplifies to 5, which is a constant polynomial because there are no variable terms in
