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Question

If the given expression is a polynomial, find its degree.
4y+7+x5/2yx1/2+2x2

A
The expression is not a polynomial and hence does not have a degree.
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B
0
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C
2
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D
3
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Solution

The correct option is D 3

4y+7+x5/2yx1/2+2x2

Simplifying the third term by adding/subtracting the exponents of same variables we get,

x5/2yx1/2=x(5/21/2)y=x4/2y=x2y

The original expression becomes

4y+7+x2y+2x2

As the exponents of all the variables are the whole number this is a polynomial and has a valid degree.

Identifying the degree of each monomial,

  1. 4y=4y1 Degree =1
  2. 7=7x0 Degree =0
  3. x2y=x2y1 Degree =2+1=3
  4. 2x2 Degree =2

The degree of the polynomial is given by the maximum degree of each monomial of the polynomial.

Here the largest degree is 3. Hence, the degree of the polynomial is 3.


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