Question

Which of the following is a polynomial ? a:- x/y. b:- x√2-3x. c:- x-²+7. d:- √2x ²+1/2 ​

Answer 1

Answer:

Answer: 4x³ + 8x

Proof:

A polynomial in x is a function of the form

a⁰ xⁿ + a¹ xⁿ¯¹ + a² xⁿ¯²……………… + aⁿ …………………………………………………..(1)

where the coefficients a⁰, a¹,……., aⁿ are constants and n is a positive integer including 0. The simplest polynomials are the powers y = x, x², x³,…., xⁿ, ………

Note that,

aⁿ can be written as aⁿx⁰

Now the given functions are:

5 + √x = 5 + x½

4x³ + 8x

3x² + 2x¯⁴

x + 50/x = x + 50x¯¹

It is seen that the only function of the form (1) is:

4x³ + 8x

which is a cubic.

∴ The cubic function 4x³ + 8x is the polynomial from among the given functions.

Aliter,

A natural way to introduce a polynomial function is through the concept of monomial since poly denotes many, several

Answer 2

Answer:

In which non-negative i.e power must be (0,1,2,3,4……….)Ex- x^0-constant polynomial

X^1-linear polynomial x^2 - quadratic polynomial etc

Solution-:1 not a polynomial because x^1/2 is not a integar .

2) polynomial because in which non-negative

Power of X

3) 3x^2+2x^-4 in which power of X=2 and -4 but - 4 is not a whole number so it is not a polynomial

4) x+50/x= x+50x^-1 here power of X=-1 is not a whole number so it is not a polynomial

Step-by-step explanation:

only for example