is y square +root2 a polynomial
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Answers
What is a polynomial?
In general words, a polynomial is the sum of the multiplications of coefficients (real numbers) and variables (like x, y) of some non - zero integral powers. It can be expressed as
a₀ xⁿ + a₁ xⁿ⁻¹ + . . . + aₙ ...(1)
where a₀, a₁, . . . , aₙ are real coefficients
Solution :
We know that, √2 is a rational number as well as it is real number.
The given expression is (y² + √2), which in general can be written as
( 1 × y² ) + ( 0 × y ) + a, where a = √2
and this is in the form of the above polynomial (1)
Therefore, the given expression is a polynomial.
Note :
The highest power of the variable present in a polynomial is called the order of the polynomial. In the given problem, the order of the polynomial is 2.
Since in the above expression , variable is y and the powers of y are positive integers. So the above expression is a polynomial with one variable.
On the other hand is not a polynomial as in the first term power of t is which is not an integer.
To be a polynomial, the powers of variable must be positive integer.
Step-by-step explanation:
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