Which of the following expressions are polynomials ? Which are not? Give reasons.
(i)` 4x ^(2) + 5x -2`
(ii) `y ^(2) -8`
(iii)5
(iv) `2x ^(2) + (3)/(x) -5`
(v) `sqrt3x ^(2) + 5y`
(vi` 1/x + 1 (x ne 0) `
(vii)` sqrtx`
(viii) 3 xyz

Which of the following expressions are polynomials in one variable and which are not ? Give reasons for you answer. (i) 3x ^(2) - 2x + 5 (ii) x ^(2) + sqrt2 (iii) p^(2) - 3p +q (iv) y + (2)/(y) (y ne 0) (v) 5 sqrtx + x sqrt5 (vi) x ^(100) + y ^(100)

Find the degree of each of the polynomials given below (i) x ^(5) - x ^(4) +3 (ii) x ^(2) + x -5 (iii) 5 (iv) 3x ^(6) + 6y ^(3) -7 (v) 4- y ^(2) (vi) 5t - sqrt3

Write the degree of each of the following polynomials (i) 7x ^(3) + 5x ^(2) + 2x -6 (ii) 7-x + 3x ^(2) (iii) 5p- sqrt3 (iv) 2 (v) - 5xy ^(2)

Classify the following as linear, quadratic and cubic polynomials (i) 5x ^(2) + x-7 (ii) x -x ^(3) (iii) x ^(2) + x + 4 (iv) x -1 (v) 3p (vi) pi r ^(2)

Determine which of the following polynomials has (x +1) as a factor. (i) x ^(3) -x ^(2) -x +1 (ii) x ^(4) - x ^(3) + x ^(2) -x +1 (iii) x ^(4) + 2x ^(3) + 2x ^(2) + x +1 (iv) x ^(3) -x ^(2) - (3- sqrt3) x + sqrt3

Find the value of the polynomial 4x ^(2) - 5x +3, at (i) x =0 (ii) x =-1 (iii) x =2 (iv) x = 1/2

Write the coefficient of x ^(2) in each of the following br> (i) 15 - 3x + 2x ^(2) (ii) 1- x^(2) (iii) pi x ^(2) - 3x + 5 (iv) sqrt2 x ^(2) + 5x -1

Find the value of each of the following polynomials for the indicated value of variables: (i) p(x) = 4x ^(2) - 3x + 7 at x =1 (ii) q (y) = 2y ^(3) - 4y + sqrt11 at y =1 (iii) r (t) = 4t ^(4) + 3t ^(3) -t ^(2) + 6 at t =p, t in R (iv) s (z) = z ^(3) -1 at z =1 (v) p (x) = 3x ^(2) + 5x -7 at x =1 (vi) q (z) = 5z ^(3) - 4z + sqrt2 at z =2

Find zeroes of the following polynomials (i) 2x -3 (ii) x ^(2) - 5x +6 (iii) x +5

Write each of the following in the form of ax + by + c = 0 and find the values of a, b and c (i) x = -5 (ii) y = 2 (iii) 2x = 3 (iv) 5y = -3