Question

Which algebraic expression is a polynomial with a degree of 2?

Answer 1

Answer:D

Step-by-step explanation:

Answer 2

Given the question "Which algebraic expression is a polynomial with a degree of 2?" and the options:
1). $4x^3-2x$
2). $10x^2- \sqrt{x}$
3). $8x^3+ \frac{5}{x} + 3$
4). $6x^2-6x + 5$

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

The degree of a polynomial is the highest exponent of the terms of the polynomial.

For option 1: It contains no fractional or negative exponent, hence it is a polynomial. But the highest exponent of the terms is 3, hence it is not of degree 2.

For opton 2: It contains a fractional exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e. $10x^2- \sqrt{x} =10x^2- x^{ \frac{1}{2} }$

For option 3: It contains a negative exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e. $8x^3+ \frac{5}{x} + 3=8x^3+5x^{-1}+3$

For option 4: It contains no fractional or negative exponent, hence it is a polynomial. Also, the highest exponent of the terms is 2, hence it is of degree 2.

Therefore, $6x^2-6x + 5$ s a polynomial with a degree of 2. [option 4]