C++ code please

starter code below

#ifndef ECPolynomial_h

#define ECPolynomial_h

#include

// *****************************************************************

// Represent a polynomial of a single variable, x, and

// support common operations on polynomial: add, scaling, multiple

// and (long) division, etc

class ECPolynomial

{

public:

// Feel free to add more interface or implementation functions

// Construct a polynomial with coefficients, where the first position is the constant term and [i] is the coefficient of x^i

// Example: given [1, 3, 0, 2], polynomial = 1 + 3x + 2x^3

// We assume listCoeffsIn is not empty

// Note: the last term in listCoeffsIn should not be zero (unless its length is 1). For example, if given [1, 3, 0], we should simply it to [1,3]. Since coefficient is a double, we consider a value is practically zero if its absolute value is sufficiently small (say less than 1e^(-10)

ECPolynomial(const std::vector &listCoeffsIn);

// Copy constructor

ECPolynomial(const ECPolynomial &rhs);

// Get the degree. Example: if polynomial=1+x+3x^3, degree=3

int GetDegree() const;

// Scale by a constant and return the resulting polynomial. For example, if polynomial is 1+3x, and

// factor = 2, the result is 2+6x

ECPolynomial Scale(double factor);

// Add a polynomial to the current polynomial (and return the result). Example: (1+2x) + (2x+3x^2) = 1+4x+3x^2

ECPolynomial operator+(const ECPolynomial &rhs) const;

// Multiply a polynomial by another polynomail and return the result. Example: (1+2x)*(1-x^2) = 1 + 2x - x^2 -2x^3

ECPolynomial operator*(const ECPolynomial &rhs) const;

// Divide a polynomial by another, and return the quotient (and save the remainder to the passed in parameter called remainder)

// Example: if we divide x^3-2x^2-4 by x-3, then quotient = x^2+x+3 and remainder is 5

// For now, assume rhs (denominator) is zero

ECPolynomial operator/(const ECPolynomial &rhs) const;

// related operator: remainder

ECPolynomial operator%(const ECPolynomial &rhs) const;

// This is for testing only. It can be useful to dump out the polynomial (in some format) to the terminal for debugging

void Dump() const;

private:

// Your code here

};

#endif /* ECPolynomial_h */

1 Polynomial You are to implement a class called ECPolynomial. This class supports common operations for a polnomial of a single variable x. In particular, 1. Scale: multiply a constant to the polynomial. 2. +: add two polynomials. 3. *: multiply two polynomials. 4. Long division: calcualte the quotient and remainder when one polynomial is divided by another polynomial. Check Wikipedia page for long division of polynomials: https://en. wikipedia.org/wiki/Polynomial_long_division. You need to support two operators: / and %. Refer to the provided starter code (the header file) for the exact signatures of the interface functions