Question

Determine whether the expression, 1/3b^3+√5b-1/4 is a polynomial or not

Answer 1

To determine whether the expression \( \frac{1}{3}b^3 + \sqrt{5}b - \frac{1}{4} \) is a polynomial, we need to look at its terms and their characteristics.

A polynomial is defined as an expression that consists of variables raised to whole number (non-negative integer) powers, with coefficients that can be real or complex numbers.

Let's analyze the given expression:

1. \( \frac{1}{3}b^3 \): This term is a polynomial term because it involves the variable \( b \) raised to the whole number power of 3, and \( \frac{1}{3} \) is a real coefficient.

2. \( \sqrt{5}b \): This term is also polynomial since \( b \) is raised to the power of 1 (which is a whole number) and \( \sqrt{5} \) is a real coefficient.

3. \( -\frac{1}{4} \): This constant term is a polynomial term because it can be viewed as \( -\frac{1}{4}b^0 \), where \( b^0 = 1 \). It has a whole number exponent (0).

All terms in the expression meet the criteria for being polynomial terms. Thus, the entire expression \( \frac{1}{3}b^3 + \sqrt{5}b - \frac{1}{4} \) is indeed a polynomial.

**Conclusion:**
Yes, the expression \( \frac{1}{3}b^3 + \sqrt{5}b - \frac{1}{4} \) is a polynomial.