Given the question "Which algebraic expression is a polynomial with a degree of 2?" and the options:
1). [tex]4x^3-2x[/tex]
2). [tex]10x^2- \sqrt{x} [/tex]
3). [tex]8x^3+ \frac{5}{x} + 3[/tex]
4). [tex]6x^2-6x + 5[/tex]
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. [tex]10x^2- \sqrt{x} =10x^2- x^{ \frac{1}{2} } [/tex]
For option 3: It contains a negative exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e. [tex]8x^3+ \frac{5}{x} + 3=8x^3+5x^{-1}+3[/tex]
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, [tex]6x^2-6x + 5[/tex] s a polynomial with a degree of 2. [option 4]
