# Highest degree of a given polynomial is

## Homework Statement

A polynomial p(x) is such that p(0)=5, p(1)=4, p(2)=9 and p(3)=20. the minimum degree it can have
a) 1 b) 2 c) 3 d) 4

## The Attempt at a Solution

a) Not Possible can't connect these points using straight line
b) Not even possible to connect these points using 2 degree polynomial
I'm confused with options c) and d)

SteamKing
Staff Emeritus
Homework Helper
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## The Attempt at a Solution

a) Not Possible can't connect these points using straight line
b) Not even possible to connect these points using 2 degree polynomial
I'm confused with options c) and d)

not so fast.....

If you want to know wether it's possible with 1st degree polynomial, compute the differences between consecutive numbers, if these are all the same, it is possible.
To do this for a 2nd degree polynomial, compute the differences between those differences, if these are all the same, it is possible. etc.

haruspex