In the following algebraic expressions, which are polynomials in one variable, which are polynomials in two variables and which are not polynomials —Let us write them.

(i) x² + 3x + 2

(ii) x² + y² + a²

(iii) y² – 4ax

(iv) x + y + 2

(v) x⁸ + y⁴ + x⁵y⁹

(vi)

(i) Since, here the highest power of variable is 1, which is a whole no.

⇒ x² + 3x + 2is a polynomial.

But here only one variable, i.e., x is used,

⇒ x² + 3x + 2 is a polynomial in one variable.

(ii) Since, here the highest power of variable is 2, which is a whole no.

x² + y² + a² is a polynomial.

Since, here two variable, i.e., x and y are used,

⇒ x² + y² + a² is a polynomial in two variables.

(iii) Since, here the highest power of variable is 2, which is a whole no.

⇒ y² – 4ax is a polynomial.

Since, here two variable, i.e., x and y are used,

⇒ y² – 4ax is a polynomial in one variable.

(iv) Since, here the highest power of variable is 1, which is a whole no.

⇒ x + y + 2 is a polynomial.

But here only two variable, i.e., x and y and are used,

⇒ x + y + 2 is a polynomial in one variable.

(v) Since, here the highest power of variable is( 5+9=14 ), which is a whole no.

(Note: 5 for x and 9 for y)

⇒ x⁸ + y⁴ + x⁵y⁹ is a polynomial.

here only two variable, i.e., x and y is used,

⇒ x² + 3x + 2 is a polynomial in two variables.

(vi) Since, here the highest power of variable is 1, which is a whole no.

⇒

And, since the exponent of variable is not zero or whole number,

⇒ is not a polynomial.