Question

If y = x³ – x² + x – 1 calculate the values of y for x = 0, 1, 2, 3, 4, 5 and form the forward differences table

Answer 1

Given y = x³ – x² + x – 1

When x = 0, y = –1

When x = 1

y = 1 – 1 + 1 – 1 = 0

When x = 2

y = 8 – 4 + 2 – 1 = 5

For x = 0, 1, 2, 3, 4, 5

When x = 3

y = 27 – 9 + 3 – 1 = 20

When x = 4

y = 64 – 16 + 4 – 1 = 51

When x = 5

y = 125 – 25 + 5 – 1 = 104

x	y	`Delta_y`	`Delta^2y`	`Delta^3y`	`Delta^4y`	`Delta^5y`
0	– 1
		1
1	0		4
		5		6
2	5		10		0
		15		6		0
3	20		16		0
		31		6
4	51		22
		53
5	104