Question

Is the expression,1/2x^3 -√3x +1, polynomial or not

Answer 1

To determine if the expression \( \frac{1}{2}x^3 - \sqrt{3}x + 1 \) is a polynomial, we need to consider the definition of a polynomial. A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients, where the coefficients are usually real numbers.

In this expression:

1. \( \frac{1}{2}x^3 \) is a polynomial term since it has a non-negative integer exponent (3).
2. \( -\sqrt{3}x \) is also a polynomial term because it has a non-negative integer exponent (1) and the coefficient \( -\sqrt{3} \) is a real number.
3. \( 1 \) is a polynomial term as well, corresponding to \( x^0 \).

Since all the terms in the expression are polynomial terms with real coefficients, the entire expression \( \frac{1}{2}x^3 - \sqrt{3}x + 1 \) is indeed a polynomial.

Thus, the expression is a polynomial.