How Do You Solve a Fourth-Degree Polynomial Temperature Model?

[Tzz]

This is one of my homework problems:
"A scientist has limited data on the temperature T during a 24-hour period. If t denotes time in hours and t = 0 corresponds to midnight, find the fourth-degree polynomial that fits the information in the following table.

t (hours) 0 10 12 16 24
T (celsius) 0 0 1 0 0

Please enter your answer as a product of linear factors. Enter any fractions or fractional coefficients as fractions, not as decimals."


I assumed the form was : T(t) = ax(x-10)(x-16)(x-24)
I found 'a' by using the given T(12)=1 and got: a = 1/1152
Multiplying out the factors i got:
T(t) = 1/1152*x^4 - 25/576*x^3 + 49/72*x^2 - 10/3*x

I'm confused as to why the program says this is the wrong answer. Maybe i have some faulty arithmetic...Any ideas?

 

[Jacobpm64]

looks fine to me *shrug*

 

[Tzz]

looks like (1/1152)x(x-10)(x-16)(x-24) worked even though it said to multiply it out...thanks anyways

 

[Jacobpm64]

yeah, that makes a lot of sense looking at the problem again

"Please enter your answer as a product of linear factors."
means that you keep it exactly as it was when it marked it correct.

x, x-10, x-16, x-24 were our linear factors, so we'd just write it as their product:

\frac{1}{1152}x(x-10)(x-16)(x-24)

 

[HallsofIvy]

looks like (1/1152)x(x-10)(x-16)(x-24) worked even though it said to multiply it out...thanks anyways

WHERE did it say "multiply it out"?