The polynomials `a x^3+3x^2-3` and `2x^3-5x+a` when divided by `(x-4)` leave the remainders `R_1a n dR_2` respectively. Find the values of a in each of the following cases
R1=R2
R1+R2=0
2R1-R2=0

The polynomial ax^(3)+3x^(2)-3 and 2x^(3)-5x+a when divided by x-1 leaves the remainders R_(1) and R_(2) respectively . Find the value of a , if 2R_(1)-R_(2)=0 .

The polynomials (x^(3)-1) and (x^(2)+1) are divided by (x+1) leave the reminder as R_(1) and R_(2) respectively. The true statement among the following is

Let R_(1) and R_(2) are the remainders when the polynomials x^(3)+2x^(2)-5ax-7 and x^(3)+ax^(2)-12x+6 are divided by x+1 and x-2 respectively.If 2R_(1)+R_(2)=6, find the value of a.

Let R_(1) and R_(2) are the remainders when the polynomials x^(3)+2x^(2)-5ax-7 and x^(3)+ax^(2)-12x+6 are divided by x+1 and x-2 respecti-vely.If 2R_(1)+R_(2)=6, find the value of a.

Consider an unknow polynomial which divided by (x - 3) and (x-4) leaves remainder 2 and 1, respectively. Let R(x) be the remainder when this polynomial is divided by (x-3)(x-4) . If equations R(x) = x^(2)+ ax +1 has two distint real roots, then exhaustive values of a are.

When a polynomial p(x) is divided by x-1, the remainder is 3. When p(x) is divided by x-3, the remainder is 5. If r(x) isthe remainder when p(x) is divided by (x-1)(x-3), then thevalue of r(-2) is

If the remainder R(x)=ax+b is obtained by dividing the polynomial x^(100) by the polynomial x^(2)3x+2 then

On dividing the polynomial f(x)=x^(3)-3x^(2)+x+2 by a polynomial g(x), the quotient q(x) and remainder r(x) where q(x)=x-2 and r(x)=-2x+4 respectively.Find the polynomial g(x) .