Question 1:

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

(i) 4x² – 3x + 7    (ii) y² + √2           (iii) 3√t + t√2

(iv) y + 2/8y        (v) x¹⁰ + y³ + t⁵⁰

Answer:

(i) 4x² – 3x + 7

Yes, this expression is a polynomial in one variable x.

(ii) y² + √2

Yes, this expression is a polynomial in one variable y.

(iii) 3√t + t√2

No. It can be observed that the exponent of variable t in term 3√t is 1/2, which is nota whole number. Therefore, this expression is not a polynomial.

(iv) y + 2/y

No. It can be observed that the exponent of variable y in term 2/y is −1, which is not a whole number. Therefore, this expression is not a polynomial.

(v) x¹⁰ + y³ + t⁵⁰

No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable.

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