A polynomial function, when divided by` x^2,` leaves remainder 1 and when divided by (x-1) leaves remainder -1. Find such polynomial of least degree.

Let p(x) be a quadratic polynomial with constant term 1. Suppose p(x) when divided by x-1 leaves remainder 2 and when divided by x+1 leaves remainder 4. Then the sum of the roots of p(x)=0 is

A polynomial P(x) when divided by (x-1) leaves a remainder of 3 when divided by (x-3) leaves a remainder of 7 and when divided by (x^(2)-4x+3) leaves a remainder f(x) .Which of the following is (are) not true? (A) f(3) = 1

A number when divided by a divisor leaves a remainder of 5and when divided divisor leaves a remainder of 45. Find the divisor

If a polynomial is divided by x-2 the remainder is 1 and when it is divided by x-3 the remainder is 2. What will be remainder when the polynomial is divided by x^(2) -5x +6 .

Find the least number which when divided by 12, leaves a remainder 7, when divided by 15, leaves a remainder 10 and when divided by 16, leaves a remainder 11

When a polynomial 2x^(3)+3x^(2)+ax+b is divided by (x-2) leaves remainder 2, and (x+2) leaves remainder -2, Find a and b.

A polynomial of degree 2 in x , when divided by (x+1),(x+2)and(x+3) , leaves remainders 1 , 4 and 3 respectively . Find the polynomial.

Find the least number which when divided by 12, 24, 36 and 40 leaves a remainder 1, but when divided by 7 leaves no remainder.

Find the least number which when divided by 15, leaves a remainder of 5, when divided by 25, leaves a remainder of 15 and when divided by 35 leaves a remainder of 25.