Which of the following is the third–degree polynomial function such that
f(0) = –24 and whose zeros are 1, 2, and 3?

f(x) = 4x^3 – 24x^2 + 44x – 24

f(x) = 2x^3 – 24x^2 + 22x – 24

f(x) = 4x^3 + 24x^2 – 44x – 24

f(x) = 2x^3 + 24x^2 – 22x – 24

Question

Which of the following is the third–degree polynomial function such that 
f(0) = –24 and whose zeros are 1, 2, and 3? 


 f(x) = 4x^3 – 24x^2 + 44x – 24 


 f(x) = 2x^3 – 24x^2 + 22x – 24 


 f(x) = 4x^3 + 24x^2 – 44x – 24 


 f(x) = 2x^3 + 24x^2 – 22x – 24

campbell_st · Answer

substitute the zeros into each function and you should have a zero remainder. 

easiest method is the use the factor theorem

check in each equation  that f(1), f(2) and f(3) = 0