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)=(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):- Which number should be added to p(x) to make (x+3)a factor of it?

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 .

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

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.

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.

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 :- Is (2x-1)a factor of p(x)? Why?

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.