The remainder is 9 when f(x) is divided by x-5 and
the remainder is -5 when f(x) is divided by x+2.
Find the remainder when f(x) is divided by (x+2)(x-5)
Let the remainder be px+q
f(5)=5p+q=9 and f(-2)=-2p+q=-5
...
p=2 and q=-1
做 polynomial 的 long division 要知道一點
when the divider is of degree n, the highest possible degree of the remainder is n-1
ie. when the divider is of degree 3, the highest possible degree of the remainder is 2
我地又知道如果x-a係factor的話,咁p(a)=0
同埋the remainder is p(b) when p(x) is divided by (x-b)
呢條題目的divider係degree 3
我地可以 let the remainder be px^2+qx+r, where p,q and r are constants.