Prove that (x-1) is a factor of `x^13-1`.

p(x)=x^2-4 x+4 a) Prove that (x-2) is a factor of p(x) . b) Prove that for any number x , p(x) is always non negative.

Check whether x - 1 is a factor of 3x^3-2x^2-3x+2 .

p(x)=(x+2)(x-3) + k ,(x-2) is a factor of p(x) :- p(x) Examine whether (x+1) is a factor of p(x).

Given x-1 is a factor of x^2+ax+b .Prove that (a+b= -1) .

Given 'x-1' is a factor of x^2+a x+b Prove that 'a+b=-1'

What is the equation of the line joining the points '(1,3),(2,7) ?' Prove that if '(x, y)' is a point on this line, so is the point '(x+1, y+4)'

If (x+1) and (x -1) are factors of x^3+2x^2 + px + q , find p and q.

If (x-1) is to be a factor of p(x) = a^2x^2-4ax + 4a-1 .What should be the value of ‘a’ ?

Consider the polynomial P(x)=ax^3-x^2-bx-1 .What is the relation between a and b if x-1 is a factor of P(x) ?

Prove that 1+cos 2x=2cos^2x .