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

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

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

p(x)=a x^3+b x^2+c x+d a) Find 'p(-1)' b) If (x+1) is a factor of 'p(x)', then prove that 'a+c=b+d' c) Write a third degree polynomial having (x+1) as a factor.

Consider the polynomial p(x)=a x^3-x^2-b x-1 a) Find 'p ( 1 )' b) What is the relation between a and 'b' if 'x-1' is a factor of 'p(x) ?' c) What is the relation between a and b if 'x+1' is a factor of 'p(x) ?' d) Will 'p(x)' have both '(x+1)' and '(x-1)' as a factors for any number a and b? Justify.

a) Find 'p(1)' if p(x)=x^2+2 x+5 b) If (x-1) is a factor of x^2+2 x+k , what number is 'k ?'

Consider the polynomial p(x)=x^3+a x^2-x+b a) Find the relation bétween 'a' and 'b' if (x-1) is a factor of p(x) b) What is the relation between 'a' and 'b' if (x-2) is a factor of p(x) ? c) Find a and 'b' so that both (x-1) and (x-2) are factors of p(x).

p(x)= ax^2+bx+5 :- If (x^2-1) is a factor of p(x),then find the value of a and b?

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

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