Write a class Poly.java to represent polynomials (ie, functions of the form axn+bxn-1+ +cx2+

dx + e). Implement the following methods:

Poly(int[] coefficient): Constructor for an array of coefficient where c[n] is the coefficient of

xn. In other words, the polynomial 2x5 + 3x4 - 8x2 + 4 would be represented by the array

[4; 0;-8; 0; 3; 2]. This way, if I want to know the coefficient of x2, I look at c[2], and get

-8. This convenience is worth the confusion that arises because we usually write arrays left-

to-right starting from the smallest index, whereas we usually write polynomials left-to-right

starting from the largest coefficient.

int degree(): Return the power of the highest non-zero term

String toString(): Overriding the Object class's toString method, this should return a String

representation of the polynomial using x as the variable, arranged in decreasing order of

exponent and printing nothing for terms with a coefficient of zero. For example, the Poly

represented by the array [4; 0;-8; 0; 3; 2] should return the string:

2x^5+3x^4-8x^2+4

Poly add(Poly a): To add two polynomials, simply add together each scale degree in turn.

Thus, (2x5 + 3x4 - 8x2 + 4) + (x3 + 4x2 - 2x) = (2x5 + 3x4 + x3 - 4x2 - 2x + 4). Create

method that constructs and returns a new Poly object with a new coecient array created

by adding the coecients of the current object and the Poly object a passed as an argument

to the add() function.

double evaluate(double x): Return the value of the function at the point x. In other words, if

the Poly object represents 2x5 +3x4 -8x2 +4 and evaluate(2.0) is called, the method should

calculate 2(2)5 + 3(2)4 - 8(2)2 + 4 and return 84.

Within the main() method of the Poly class, create a series of tests which exercise each of these

methods and report their success or failure.