Question

Which algebraic expression is a polynomial? 3m2n – StartFraction 2 m Over n EndFraction + StartFraction 1 Over n EndFraction StartFraction 2 m n Over 5 EndFraction – StartFraction StartRoot m EndRoot Over 4 EndFraction + 4m5 StartFraction 4 m cubed Over n squared EndFraction – 3mn5 + StartRoot 8 EndRoot 7mn + StartFraction 3 m Over 2 EndFraction + StartFraction 5 n Over 4 EndFraction

Answer 1

Answer:

d

Step-by-step explanation:

Answer 2

Out of all options, the 4th option $7mn + \dfrac{3m}{2} + \dfrac{5n}{4}$ is polynomial, rest are not polynomial.

Given expressions are:

A:  $3m^2n - \dfrac{2m}{n} + \dfrac{1}{n}$

B:  $\dfrac{2mn}{5} - \dfrac{\sqrt{m}}{4} + 4m^5$

C:  $\dfrac{4m^3}{n^2} - 3mn^5 + \sqrt{8}$

D: $7mn + \dfrac{3m}{2} + \dfrac{5n}{4}$

What is a polynomial?

Sum of such algebraic expressions which contains variables with non negative integer powers and real number coefficients is a polynomial.

By that definition, all the options except option D are not polynomial.

Option A contains n in denominator.

Option B contains square root of m.

Option C contains n in denominator.

Option D is polynomial as it satisfies the definition.

Thus, out of all options, the 4th option $7mn + \dfrac{3m}{2} + \dfrac{5n}{4}$ is polynomial, rest are not polynomial.

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