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`

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

Determine which of the following polynomials has (x + 1) as a factor. x^(3)-x^(2)-x+1

Determine which of the following polynomials has (x + 1) as a factor. x^(4)+2x^(3)+2x^(2)+x+1

Determine which of the following polynomials has (x + 1) as a factor. x^(3)-x^(2)-(3-sqrt(3))x+sqrt(3)

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-sqrt(3))x+sqrt(3)

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

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)

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

Check whether the following equations are quadratic or not . (i) x^(2) - 6x - 4 = 0 (ii) x^(3) - 6x^(2) + 2 x - 1 = 0 (iii) 7x = 2x^(2) (iv) x^(2) + (1)/(x^(2)) = 2 (v) (2x + 1 ) (3 x + 1 ) = 6 (x - 1) (x - 2) (vi) 3y^(2) = 192