POLYNOMIAL (P) OR NON-POLYNOMIAL (NP)?
1. 5
2. -2x^2
3. (3/4)x + 21
4. 5x^2 - 4xy + 2y^2
5. a^(-2) + 4
6. sqrt(9h)
7. sqrt(25)
8. (2/k) + 14
9. 1/4
10. 10 - b^(1/2)
Answer (1)
Let's analyze each expression one by one to determine if it's a polynomial or not.
5 : This is a constant, which is a polynomial. In general, any single number can be considered a polynomial of degree 0.
-2x^{23} : This is a monomial (a single term) where the variable is raised to a non-negative integer power. Thus, it is a polynomial.
\frac{3}{4}x + 21 : This is a linear polynomial, as it has a term with a variable raised to the first power plus a constant.
5x^2 - 4xy + 2y^2 : Each term is a product of constants and variables to non-negative integer powers. This is a polynomial.
a^{-2} + 4 : This expression includes a − 2 , which is a negative power. Polynomials cannot have variables with negative exponents, so this is not a polynomial.
\sqrt{9h} : This part can be rewritten as ( 9 h ) 1/2 , which means the variable h is raised to a non-integer power ( 1/2 ). Therefore, this is not a polynomial.
\sqrt{25} : This equals 5 , which is a constant, thus it is a polynomial.
\frac{2}{k} + 14 : The term k 2 is equivalent to 2 k − 1 , indicating a negative exponent on the variable. This is not a polynomial.
\frac{1}{4} : This is a constant number, which is a polynomial of degree 0.
10 - b^{1/2} : The term b 1/2 involves a variable raised to a non-integer power. Hence, this is not a polynomial.
To summarize:
Polynomial
Polynomial
Polynomial
Polynomial
Non-Polynomial
Non-Polynomial
Polynomial
Non-Polynomial
Polynomial
Non-Polynomial
