Multiplication of polynomials in c++

I enter an array and the code should multiply this array by (x^2 + 2*A*X + A^A). for example an array 1, 3, 3, 1 should have answer 1, 5, 10, 10, 5, 1 if A = 1. I have tried to write the code but I have no idea how I am supposed to multiply polynomials in C++.

CODE

#include "pch.h"
#include <iostream>

int main()
{
int a, n;

std::cout << "Enter the Power n: ";
std::cin >> n;

std::cout << "Enter the number A: ";
std::cin >> a;

int arr_size = n + 1;       

int *array = new int[2 * arr_size];

std::cout << "Enter the array P(X): ";

for (int i = 0; i < arr_size; i++)
{
    std::cin >> array[i];
}

for (int i = 0; i < arr_size; i++)
    std::cout << array[i] << " ";

const int x = 1;
for (int i = 0; i < arr_size; i++) {
    array[i] = array[i] * x ^ 2;
    array[i] = array[i] * (2 * a*x);
    array[i] = array[i] * (a * a);

    std::cout << array[i] << " ";
}
return 0;
}