Question

Which of the following expressions are polynomials?

a) 9b⁶c
b) 36x² − 2x⁹
c) 8x⁷ − 5x⁴
d) 7x³ − 2x²

Answer 1

To determine which of the given expressions are polynomials, we need to check if they meet the definition of a polynomial. Polynomials consist of variables and coefficients combined using addition, subtraction, and multiplication.

Step-by-step explanation:

A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division by a variable. To determine which of the given expressions are polynomials, we need to check if they meet this definition.

1. a) 9b⁶c: This is a polynomial because it consists of variables (b and c) raised to non-negative integer exponents (6 and 1, respectively).
2. b) 36x² − 2x⁹: This is NOT a polynomial because it contains a variable (x) raised to a negative exponent (⁹).
3. c) 8x⁷ − 5x⁴: This is a polynomial because it consists of a variable (x) raised to non-negative integer exponents (7 and 4).
4. d) 7x³ − 2x²: This is a polynomial because it consists of a variable (x) raised to non-negative integer exponents (3 and 2).

Therefore, the polynomials among the given expressions are a) 9b⁶c, c) 8x⁷ − 5x⁴, and d) 7x³ − 2x².