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

Consider the polynomial P(x)=ax^3-x^2-bx-1 Will, P(x) have both (x+1) and (x-1) as factors for any numbers 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).

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

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.

For p(x)= 2 x^ 2 − 3 x + 1 , find p(0),p(1),p(-1)

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’ ?

Given that x^(2)+x-6 is a factor of 2x^(4)+x^(3)-ax^(2)+bx+a +b-1 , find the values of a and b.

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