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)

Answer :

(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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