(i) x^3-5x+2
soln:- The given Expression is x^3-5x+2.
In this Expression having only non-negative integral powers of x.so,it is a polynomial.The highest power of x is 3.
So,it is a polynomial of degree 3.
(ii) y^2+√2y-√5
soln:- The given Expression is y^2+√2y-√5
In this Expression having only non-negative integral powers of y.so,it is a polynomial.
The highest power of y is 2.
So,it is a polynomial of degree 2.
(iii) 2√x + 7
soln:- The given Expression is 2√x + 7
In this Expression having not non-negative integral powers of x.so,it is not a polynomial.
(iv) -6.
soln:-let the Expression is -6x^0.
In this Expression having only non-negative integral powers of x.so,it is a polynomial.
The highest power of x is 0.
So,it is a polynomial of degree 0.
(v) 4t^2+(1/2)t+2√3.
soln:- The given Expression is 4t^2+(1/2)t+2√3.
In this Expression having only non-negative integral powers of t.so,it is a polynomial.
The highest power of t is 2.
So,it is a polynomial of degree 2.
(vi) z^2+(5/z^2)+1
soln:-we can write this Expression is z^2+(5z^-2)+1
In this Expression having not non-negative integral powers of z.so,it is not a polynomial.
(vii) 1/3x
soln:-we can write this Expression is 1(3x^-1)=3x^-1
In this Expression having not non-negative integral powers of t.so,it is not a polynomial.
(viii) 1-√(5x)
soln:-we can write this Expression is 1-(√5)(x)^1/2
In this Expression having not non-negative integral powers of x.so,it is not a polynomial.
(ix) {1/(4x^-2)}+3x+5
soln:-we can write this Expression is {1/(4x^-2)}+3x+5= (4x^2)+3x+5.
In this Expression having only non-negative integral powers of x.so,it is a polynomial.
The highest power of x is 2.
So,it is a polynomial of degree 2.
(x)[ 6√x + {x^(3/2)}]/√x
soln:-we can write this Expression is[ 6√x + {x^(3/2)}]/√x
= 6√x/√x + {x^(3/2)}/x^1/2
=6+x^(3/2)-(1/2)
=6+x
=x+6
In this Expression having only non-negative integral powers of x.so,it is a polynomial.
The highest power of x is 1.
So,it is a polynomial of degree 1.
