Grade 12 Math Homework Need Help 10 Points Best Answer?
Im studying for my test tomorrow on Polynomials, and the practice sheet gives me the polynomial with the points (1,0), (2,10), (3, 42), (4,108) (5, 220), (6, 390).
What is the equation? What is the equation in factored form? And how did you get it?
- Roger the MoleLv 79 years agoFavorite Answer
With six points the highest possible degree polynomial that can be determined is a 5th degree. The model for that is:
Ax^5 + Bx^4 + Cx^3 + Dx^2 + Ex + F = y
Take each of the six points, one at a time, and generate an equation by substituting x and y into the model equation:
A + B + C + D + E + F = 0
32A + 16B + 8C + 4D + 2E + F = 10
243A + 81B + 27C + 9D + 3E + F = 42
1024A + 256B + 64C + 16B + 4A + F = 108
3125A + 625B + 125C + 25B + 5A + F = 220
7776A + 1296B + 216C + 36B + 6A + F = 390
Solve these six equations simultaneously:
A = 0
B = 0
C = 2
D = -1
E = -1
F = 0
So the desired polynomial is:
2x^3 - x^2 - x = y
In retrospect, it would have saved effort to have prepared a table of successive differences to determine at the beginning that only a cubic equation was necessary.