Question

***CONTENT QUALITY REQUIRED***
SPAM ANSWERS WILL BE REPORTED

Answer 1

let f (x) be a polynomial, then f (x)=
$a {x}^{3} + b {x}^{2} + cx + d$
now when it is divided by (x-1) the remainder is 5...
this implies that f (1)=5......


again when f(x) is divided by (x-2) then the the remainder is 7...
f (2)=7......
now
let the remainder when f (x)is divided by (x-1)(x-2) be (Ax+B).....with the quietiont q (x)
f (x) = q(x)(x-1)(x-2)+(Ax+B)
f (1) = 0+(A(1)+B) = 5
A+B=5........
f (2) =0+(A (2)+B)=7
2A+B=7.......
SUBTRACTING THESE EQUATION
WE GET
A=2;B=3
HENCE THE REMAINDER =Ax+B=2x+3