Question

Please help......

1. What polynomial is represented in the given values below?
Please show your differences
Please show your calculations to determine your coefficients

2 0 4 14 30

-2 -4 -4 10 50



2. Choose a cubic polynomial- any cubic polynomial

Substitute x = 0, x=1, x=2 and x=3
Fill out the chart below
Write your results in a pattern left to right (just like #1 and #2)
Find the 1st, 2nd and 3rd Differences
Calculate a, b, c and d using the ax³+bx²+cx+d chart - show your work!
Your results for a, b, c and d should match your original polynomial.

Your polynomial__________________________________

x =
0
1
2
3

ax²+bx+c
Quadratic polynomial

ax³+bx²+cx+d
Cubic polynomial

Answer 1

2 0 4 14 30

Explanation:

Answer 2

(1)

f(x) = ax^3 + bx^2 + cx + d

In table attached, x and f(x) values are shown

a = 3rd difference/3! = 12/6 = 2

f(0) = d = -4

f(2) = 2(2)^3 + b(2)^2 + c(2) - 4 = -2

12 + 4 b + 2 c = -2

4 b + 2 c = -14 (eq. 1)

f(4) = 2(4)^3 + b(4)^2 + c(4) - 4 = -4

128 + 16 b + 4 c - 4 = -4

16 b + 4 c = -128 (eq. 2)

Multiplying eq. 1 by 2 and then subtracting it to eq. 2 gives

8 b = -100

b = -12.5

Replacing in eq. 1

4(-12.5) + 2 c = -14

2 c = 36

c = 18

The polynomial is 2x^3 - 12.5x^2 + 18x - 4

(2)

My polynomial: x^3 + x^2 + x + 1

In table attached, x and f(x) values are shown

a = 3rd difference/3! = 6/6 = 1

f(0) = d = 1

f(1) = (1)^3 + b(1)^2 + c(1) + 1 = 4

1 + b + c + 1 = 4

b + c = 2 (eq. 1)

f(2) = (2)^3 + b(2)^2 + c(2) + 1 = 15

8 + 4 b + 2 c + 1 = 15

4 b + 2 c = 6 (eq. 2)

Multiplying eq. 1 by 2 and then subtracting it to eq. 2 gives

2 b = 2

b = 1

Replacing in eq. 1

(1) + c = 2

c = 1