Q. 24.4( 11 Votes )

In the following polynomials, let us write which are first degree polynomials in one variable, which are second degree polynomials in one variable and which are third degree polynomials in one variable.

(i) 2x + 17

(ii)x3 + x2 + x+ 1

(iii) –3 + 2y2 + 5xy

(iv)5 – x – x3

(v)

(vi)

Answer :

(i) (Note: The degree is the value of the greatest (highest) exponent of any expression (except the constant) in the polynomial. To find the degree all that you have to do is find the largest exponent in the polynomial).

Since, here the highest power of variable(x) is 1,


2x + 17 is a first degree polynomial.


(ii) Since, here the highest power of variable(x) is 3,


x3 + x2 + x+ 1 is a third degree polynomial.


(iii) Since, here the highest power of variable(x, y) is 2,


–3 + 2y2 + 5xy is a second degree polynomial.


(Note: Whenever we have polynomial in two variable (i.e., x and y) and both are in multiplication we see for the degree by adding the powers of both the variable.)


(iv) Since, here the highest power of variable(x) is 3,


5 – x – x3 is a third degree polynomial.


(v) Since, here the highest power of variable (t) is 2,


√2 +t+t2 is a second degree polynomial.


(vi) Since, here the highest and only power of variable(x) is 1,


√ 5x is a first degree polynomial.


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