Question

Which algebraic expression is a polynomial?

a. 4x² - 3x + 2/x
b. -6x³ + x² - √5
c. 8x² + √x
d.-2x⁴ +3/2x

Answer 1

The algebraic expression that is a polynomial among the given options is `-6x^3 + x^2 - √5`. It satisfies the conditions of a polynomial by having variables raised to non-negative integer exponents and combining terms using addition and subtraction.

Step-by-step explanation:

The question asks which algebraic expression is a polynomial. A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents of variables, combined using addition, subtraction, and multiplication. Considering the provided options:

1. 4x2 - 3x + 2/x is not a polynomial because it contains a term with the variable in the denominator.
2. -6x3 + x2 - √5 is a polynomial. It contains terms with variables raised to non-negative integer exponents and also includes a constant term √5.
3. 8x2 + √x is not a polynomial because the square root of x implies a fractional exponent, which is not allowed in polynomials.
4. -2x4 +3/2x is ambiguous and could be interpreted as a polynomial if it means (-2x4) + (3/2)x, but it could also be non-polynomial if interpreted as -2x4 + 3/(2x).

Therefore, the algebraic expression -6x3 + x2 - √5 is a polynomial.