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`

Write the coefficient of x ^(3) in each of the following (i) x ^(3) + x +1 (ii) 2- x ^(3) + x ^(2) (iii) sqrt2 x ^(3) + 5 (iv) 2x ^(3) +5 (v) pi/2 x ^(3) +x (vi) - 2/3 x ^(3) (vii) 2x ^(2) +5 (viii) 4

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)

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

Use the Factor Theorem to determine whether g (x) is factor of f(x) in each of the following cases: (i) f (x) = 5x ^(3) + x ^(2)-5x -1, g (x)=x +1 (ii) f (x) = x ^(3) + 3x ^(2) + 3x +1 , g(x) =x +1 (iii) f (x) =x ^(3) - 4x ^(2) +x + 6, g (x) =x -2 (iv) f (x) = 3x ^(3) - 20x + 12, g (x) = 3x -2 (v) f (x) = 4x ^(3) + 20 x ^(2) + 33 x +18, g (x) =2x +3

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

Solve the following : (i) |x-2|=(2-x) " (ii) " |x+3| = -x-3 (iii) |x^(2)-x|=x^(2)-x " (iv) " |x^(2)-x-2| =2+x-x^(2)

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

The coefficient of x^3 in the expansion of (1-x+x^2)^5 is

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 domain and range of the following functions. (i) f(x)=sqrt(2x-3) " (ii) " f(x) =(1)/(x-2) (iii) f(x) =x^(2) +3 " (iv) " f(x)=(1)/(x^(2)+2)