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Mathematics

Identify which of the following algebraic expressions are polynomials. If so, write their degrees.

(i) 23x2−57x−14\dfrac{2}{3}x^2 - \dfrac{5}{7}x - \dfrac{1}{4}

(ii) 3x2+2x−33x^2 + \dfrac{2}{x} - 3

(iii) x2−23x7−5x8x^2 - \dfrac{2}{3}x^7 - 5x^8

Algebra Basics

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Answer

An algebraic expression is a polynomial only when the powers of the variable are non-negative integers.

(i) 23x2−57x−14\dfrac{2}{3}x^2 - \dfrac{5}{7}x - \dfrac{1}{4}

Since the highest power of x in the expression is 2, the expression is a polynomial with degree 2.

(ii) 3x2+2x−33x^2 + \dfrac{2}{x} - 3

Power of x is negative, so it is not a polynomial.

It is not a polynomial.

(iii) x2−23x7−5x8x^2 - \dfrac{2}{3}x^7 - 5x^8

Since the highest power of x is 8, the expression is a polynomial with degree 8.

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