Question

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

i) 3x² – 2x + 5

ii) x² + √2

iii) p² – 3p + q

iv) y + 2/y

v) 5√x + x√5

vi) x¹⁰⁰ + y¹⁰⁰

Answer 1

i) Given expression is a polynomial in one variable.

ii) Given expression is a polynomial in one variable.

iii) Given expression is not a polynomial in one variable. It involves two variables p and q.

iv) Given expression is not a polynomial. Since the second term contains the variable in its denominator.

v) Given expression is not a polynomial. Since the first term’s exponent is not an integer.

vi) Given expression has two variables. So it is not a polynomial in one variable.