Q. 85.0( 7 Votes )

# 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.

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