Q. 24.1( 31 Votes )

# Which of the following expressions are polynomials in one variable and which are not? Give reasons for your answer.

(i) 3x^{2} - 2x + 5

(ii) x^{2} + √2

(iii) p^{2} - 3p + q

(iv)

(v)

(vi) x^{100} + y^{100}

Answer :

(i) 3x^{2} - 2x + 5 has only one variable that is x.

∴ yes, it is a polynomial in one variable.

(ii) x^{2} + √2 has only one variable that is x.

∴ yes, it is a polynomial in one variable.

(iii) p^{2} – 3p + q has two variables that are p and q.

∴ no, it is not a polynomial in one variable.

(iv) has a negative exponent of y.

∴ no, it is not a polynomial.

(v) The exponent of x in 5√x + x√5 is 1/2 which is not a non-negative integer

∴ no, it is not a polynomial.

(vi) x^{100} + y^{100} has two variables that are x and y.

∴ no, it is not a polynomial in one variable.

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