Divide p(x) by g(x), where `p(x) = x+3x^(2) -1` and `g(x) = 1+x`.

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

Divide 2x^(2)+3x+1 by x+2 .

Let for a != a_1 != 0 , f(x)=ax^2+bx+c , g(x)=a_1x^2+b_1x+c_1 and p(x) = f(x) - g(x) . If p(x) = 0 only for x = -1 and p(-2) = 2 then the value of p(2) .

Find the values of x for which the functions f(x)= 3x^(2)-1 and g(x)= 3 + x are equal

If alpha, beta (where alpha lt beta ) are the points of discontinuity of the function g(x) = f(f(f(x))), where f(x) = (1)/(1-x), and P(a, a^(2)) is any point on XY - plane. Then, The domain of f(g(x)), is

Divide 3x ^(2) + x-1 by x +1

Verify whether the values of x given in each case are the zeroes of the polynomial or not ? (i) p (x) = 2 x + 1,x =- 1/2 (ii) p (x) = 5x -pi , x = (-3)/(2) (iii) p (x) = x ^(2) -1 , x = pm 1 (iv) p (x) = (x-1) (x +2) , x =-1,k-2 (v) p (y) = y ^(2) , y =0 (vi ) p (x) = ax + b, x =- (b)/(a) (vii) f (x) = 3x ^(2) -1 , x =- (1)/(sqrt3) , (2)/(sqrt3) (viii) f (x) =2x -1 , x = (1)/(2), (-1)/(2)

The value of p(x) = x^(3) + x^(2) - 3x-3 at x = -1 is …… .

Divide 2x^(2)+3x+1" by "x+2 .

Find the remainder when p (x) = x ^(3) - 6x ^(2) + 14x -3 is divided b y g (x) =1-2x and verify the result by long division.