Phrases 1, 2, and 5 are considered polynomials, while phrases 3 and 4 are not.
Yes, mathematical phrases can be considered polynomials if they meet the following criteria:
The expression consists of variables, constants, and exponents.
The exponents of the variables are non-negative integers.
The expression is combined using arithmetic operations (addition, subtraction, multiplication, and division), but division by a variable is not allowed.
Based on these criteria, here's an analysis of the given mathematical phrases:
3x^2 - 2x - 10: This is a polynomial because it consists of variables (x), constants (3, -2, and -10), and exponents (2 for x). The exponents are non-negative integers.
(x + 2)(x - 3): This is a polynomial because it is the product of two polynomials (x + 2 and x - 3), each of which satisfies the criteria for a polynomial.
1/x: This is not a polynomial because it involves division by a variable (x).
√x: This is not a polynomial because it involves a non-integer exponent (1/2) for the variable (x).
e^x: This is a polynomial if we consider "e" as a constant. In that case, the expression consists of a variable (x), a constant (e), and an exponent (x). The exponent is non-negative, and the expression is combined using exponentiation. However, if "e" is considered a variable, then the expression is not a polynomial because the exponent is not an integer.
Therefore, phrases 1, 2, and 5 are considered polynomials, while phrases 3 and 4 are not.
Question
Will you consider these mathematical phrases as polynomials ? Why or why not?