With the given set of points, determine the equation of the polynomial function using the algebraic method.

(1,1), (2,10), (3,42), (4,111), (5,231), (6,416)

x y 1st 2nd 3rd

1 1 - - -

2 10 9 - -

3 42 32 23 -

4 111 69 37 14

5 231 120 51 14

6 416 185 65 14

11=a+b+c+d

210=8a+4b+2c+d

342=27a+9b=3c+d

4111=64a+16b+4c+d

2-19=7a+3b+c

3-232=19a+5b+c

4-369=37a+7b+c

6-523=12a+2b

7-637=18a+2b

9-814=6a

What I have so far doesn't seem right....