When the polynomial `f(x)=ax^(2)+bx+c` is divided by x , x - 2 and x +3 remainders obtained are 7 , 9 and 49 respectively . Find the value of `3a + 5b+ 2c`.

When the polynomial p(x)=ax^(2)+bx+c is divided by (x-1) and (x+1) , the remainders obtained are 6 and 10 respectively . If the value of p (x) is 5 at x = 0, then the value of 5a-2b+5c is ______.

A quadratic polynomial ax^(2) + bx + c is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b) ?

The polynomial f (x)= x^4 + 2 x^3 + 3 x^2 - ax + b when divided by (x-1) and (x + 1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when f (x) is divided by (x-2)

If the polynomial f(x)=2x^(3)+ax^(2)+bx-2 be divided by (2x - 3) and (x - 1), the respective remainders are 30 and 0. Calculate the values of a and b.

The polynomials f(x)=x^(4)-2x^(3)+3x^(2)-ax+b when divided by (x-1) and (x+1) leaves the remainders 5 and 19 respectively.Find the values of a and b..Hence,find the remainder when f(x) is divided by (x-2)^( ? )

If the polynomial ax^(5)-23x^(2)+47x+1 is divided by x -2then remainder is 7. Find the value of a.

If ax^(2) +bx+c is divided by x+3,x-5, and x-1, the remainders are 21, 61 and 9 respectively. Find a,b, and c. (Use Gaussian elimination method. )

The polynomials f(x)=x^4-2x^3+3x^2-ax+b when divided by (x-1) and (x+1) leaves remainder 5 and 19 respectively. Find the value of a and b hence, find the remainder when f(x) is divided by (x-2)

When a polynomial P(x) is divided by x,(x-2) and (x-3), remainders are 1,3 and 2 respectively.If the same polynomial is divided by x(x-2)(x-3), the remainder is ax^(2)+bx+c, then the value of c is