$4.$ Develop a forward difference table for the following data:

X Y

$2-7$

$4-3$

$66$

$825$

$1062$

$12129$

Once you complete the difference table, answer the following questions.

a$)$ Give a polynomial of degree $2$ using the Newton$$s difference table that can be used for implementation.

b$)$ Check how accurate the polynomial solution is by evaluating the polynomial expression at x $=5,$ check against the correct value of $0\mathrm{.}6495$

Find the relative percentage error.