Math Is Fun Forum

Here the tricky questions:D

1(a) (POLYNOMIAL)
Determine the polynomial ƒ(x) satisfying the following conditions:

i)   Degree ƒ(x) is four
ii)  (x-1) is a factor of ƒ(x) and ƒ'(x)
iii)  ƒ(0)=3 and f'(0)=-5
iv)  when ƒ(x) is divided by (x-2), the remainder is 13

Hence, factorize ƒ(x) completely and solve the equation ƒ(x)=0.