Factorise the expression
`3cos^2 x-11 cosx-4`

Using the Remainder theorem, factorise the expression 2x^(3)+x^(2)-2x-1 completely.

Using the Factor theorem, show that (i) (x-2) is a factor of x^(3)-2x^(2)-9x+18 . Hence factorise the expression x^2-2x^2-9x+18 completely. (ii) (x+5) is a factor of 2x^3+5x^2-28x-15 . Hence factorise the expression 2x^3+5x^2-28x-15 completely. (iii) (3x+2) is a factor of 3x^(3)+2x^(2)-3x-2 . Hence factorise the expression 3x^3+2x^2-3x-2 completely.

Factorise the given expression completely: 6x^(2) + 7x -5

Show that 2x+7 is a factor of 2x^(3)+5x^(2)-11x-14 . Hence factorise the given expression completely, using the factor theorem.

5. if the expression cos^2(pi/11)+cos^2((2pi)/11)+cos^2((3pi)/11)+cos^2((4pi)/11)+cos^2((5pi)/11) has the value equal to p/q in it lowest from ; then find (p+q)

Use the Remainder Theorem to factorise the following expression 2x^(3)+x^(2)-13x+6 .

The expression 4x^(3)-bx^(2)+x-c leaves remainders 0 and 30 when divided by x+1 and 2x-3 respectively. Calculate the values of b and c. Hence factorise the expression completely.

If x_(1),x_(2),...,x_(n) are real numbers, then the largest value of the expression sinx_(1)cosx_(2)+sinx_(2)cosx_(3)+...+sinx_(n)cosx_(1), is

The expression 4cos^(4)x-2cos2x-(1)/(2)cos4x when simplified reduces to :

If the expression exp {1+|cosx|+cos^(2)x+|cos^(3)x|+ . . . . oo)log_(e)4} satisfies the equation y^(2)-20y+64=0" for "0ltxltpi , then the set of value of x is