A certain polynomial P(x), x in R when divided by x-a ,x-b and x-c leaves remainders a , b , and c , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c) where a, b, c are distinct.

A certain polynomial P(x)x in R when divided by x-a ,x-ba n dx-c leaves remainders a , b ,a n dc , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c)w h e r eab, c are distinct.

If a polynomial f (x) is divided by (x - 3) and (x - 4) it leaves remainders as 7 and 12 respectively, then find the remainder when f (x) is divided by (x-3)(x-4) .

If 8x^(3) - 14x^(2) - 19x - 8 is divided by 4x+ 3 then find the quotient and the remainder.

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.

If f(x)=x^3-3x^2+2x+a is divisible by x-1, then find the remainder when f(x) is divided by x-2.

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.

When the positive integers a, b and c are divided by 13 the respective remainders are 9, 7 and 10. Find the remainder when a+2b+3c is divided by 13.

When the positive integer a, b, c and are divided by 13 the respective remainders are 9, 7 and 10. Find the remainder when a+2b+3c is divided by 13.

A boy is walking along the path y=ax^(2)+bx+c through the points (-6,8) (-2,-12) and (3,8). He wants to meet his friend at P(, 7,60) . Will he meet his friend? (Use Gaussian elimination method.)