Answer:
d) [tex]7mn+\frac{3m}{2}+\frac{5n}{4}[/tex]
Step-by-step explanation:
Which algebraic expression is a polynomial?
[tex]a)3m^2n-\frac{2m}{n}+\frac{1}{n} \\b)\frac{2mn}{5}-\frac{\sqrt{m} }{4} +4m^5\\c)\frac{4m^3}{n^2}-3mn^5+\sqrt{8}\\d)7mn+\frac{3m}{2}+\frac{5n}{4}[/tex]
Answer: A polynomial is an expression with variables and coefficients separated by addition and subtraction. The following are used when determining if an expression is a polynomial:
i) Variables of a polynomial must not have negative exponent.
ii) Variables of a polynomial must not have fractional exponent.
iii) Dividing by an exponent is not allowed
iv) Exponent radicals are not allowed.
a) [tex]3m^2n-\frac{2m}{n}+\frac{1}{n}[/tex] is not a polynomial because dividing by an exponent is not allowed.
b) [tex]\frac{2mn}{5}-\frac{\sqrt{m} }{4} +4m^5[/tex], is not a polynomial because exponent radicals are not allowed (√m)
c) [tex]\frac{4m^3}{n^2}-3mn^5+\sqrt{8}[/tex] is not a polynomial because dividing by an exponent is not allowed.
d) [tex]7mn+\frac{3m}{2}+\frac{5n}{4}[/tex] is a polynomial
