the polynomial f(x)=a(x-1)^2+b(x+2)^2 is divided by x+1 and x-2 the remainders are 3 and-15 respectively find the value of a and b

Answer 1

f(x)=a(x-1)^2+b(x+2)^2
given:
f(-1) = 3
a(4) + b(1) = 3 -----> 4a + b = 3

f(2) = -15
a + 16b = -15 or a = -15-16b
substitute:
4(-15-16b) + b = 3
-60 - 64b + b = 3
-63b = 63
b = -1 , then a = -15 + 16 = 1