Which one of the following is a polynomial
a. x²/2 - 2/x²
b. √2x - 1
c. x² + 3x3/2/ √x
d. (x - 1)/ (x + 1)
Solution:
Let us simplify each option
a. x²/2 - 2/x²
= x²/2 - 2x-2
As one of the exponents of x is -2 which is not a whole number, it is not a polynomial.
b. √2x - 1
= √2x1/2 - 1
As the exponent of x is 1/2 which is not a whole number, it is not a polynomial.
c. x² + 3x3/2/ √x
= x² + 3x3/2 - ½
= x² + 3x
As the exponent of x is the whole number, it is a polynomial.
d. (x - 1)/ (x + 1)
As it is a rational function, it is not a polynomial.
Therefore, x² + 3x3/2/ √x is a polynomial.
✦ Try This: If x² + kx + 6 = (x + 7) (x + 8) for all x, then the value of k is
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 1
Which one of the following is a polynomial? a. x²/2 - 2/x², b. √2x - 1, c. x² + 3x3/2/ √x, d. (x - 1)/ (x + 1)
Summary:
A polynomial is a type of expression in which the exponents of all variables should be a whole number. x² + 3x3/2/ √x is a polynomial
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