A polynomial function p of degree 3 contains the points (0, –4), (1, 5), (2, 24), and (3, 59).
Find an equation for p

Question

A polynomial function p of degree 3 contains the points (0, –4), (1, 5), (2, 24), and (3, 59). 
Find an equation for p

anonymous · Answer

$$p(x)=ax^3+bx^2+cx+d$$

so this is a problem of interpolation:

$$p(0)=-4$$
$$p(1)=5$$
Can you do the missing ones?

anonymous · Answer

yes,  Thank you :)

anonymous · Answer

very good!

anonymous · Answer

but then how do put them into the equation for p?

anonymous · Answer

well it will give you a 4x4 system with a,b,c,d. Solve for them and then plug back into the original equation p(x). That will give you the solution of a polynomial that has the desired characteristics.

anonymous · Answer

It will also give you some easy ones, p(0)=-4 leads to d=-4

anonymous · Answer

So you're actually left with a 3x3 system out of that.