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).

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) ?

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) ?

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.

Consider the polynomial P(x)=ax^3-x^2-bx-1 .Find P(1) .

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

Consider the polynomial p(x)= x^2-5x+6 :- Find the remainder when p(x) is divided by (2x-1).

Consider the polynomial P(x)= x^2-kx-7 :- IfP(1) = 3, Find the value of k.

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

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).

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