题目不难，但有几个需要注意一点的地方：

1.当用户输入或者计算出来的多项式中某一项系数为0不用输出

2.系数为1或者-1的时候，1是不需要展现在x前面

3.正数在第一个数的时候不能有+

（前面两个图已经表示出来了。）

然后下面就是实现的代码供参考

首先class一个类，私有数据为保存指数的值，一个指针用来表示动态数组（也就是存放多项式系数的地方），x的具体值，以及最后x带入计算的结果

公共部分主要就是重载一下加法和减法，一个展示结果输出的类方法

#include<iostream>
#include<numeric>
#include<limits>
#include<cstdlib>
class Poly
{
public:Poly(unsigned long long _index);Poly(unsigned long long _index,double _point);~Poly(void);friend Poly operator+(const Poly& r1, const Poly& r2);friend Poly operator-(const Poly& r1, const Poly& r2);void showexpression(void)const;bool getarray(void);void getpointans(void);private://这两个字符是输出给用户看x多少次方char m_showtouser_character1;char m_showtouser_character2;//x的具体值double m_point;//最高指数unsigned long long m_index;//保存系数的数组double* m_indexarray;//计算所得结果double m_ans;
};
Poly::Poly(unsigned long long _index)
{m_showtouser_character1 = 'x';m_showtouser_character2 = '^';m_indexarray = new double[_index + 1];m_index = _index;m_point = 0;m_ans = 0;
}
Poly::Poly(unsigned long long _index,double _point)
{m_showtouser_character1 = 'x'; m_showtouser_character2 = '^';m_indexarray = new double[_index+1];m_index = _index;m_point = _point;m_ans = 0;
}Poly::~Poly(void)
{
}
//这个show我实在是没办法，太长了
void Poly::showexpression(void) const
{unsigned long long tempindex = m_index, checkforindexarrayiszero = 0;//排除特殊的三种情况if (m_indexarray[0] == 1 || m_indexarray[0] ==-1 || m_indexarray[0]== 0){if (m_indexarray[0] == -1){if (m_index == 1)std::cout << '-'<<m_showtouser_character1;elsestd::cout << '-' << m_showtouser_character1 << m_showtouser_character2 << tempindex;}if (m_indexarray[0] == 1){if (m_index == 1)std::cout << m_showtouser_character1;elsestd::cout << m_showtouser_character1 << m_showtouser_character2 << tempindex;}if (m_indexarray[0] == 0)checkforindexarrayiszero = 1;}else{if (m_index != 1)std::cout << m_indexarray[0] << m_showtouser_character1 << m_showtouser_character2 << tempindex;elsestd::cout << m_indexarray[0] << m_showtouser_character1;}tempindex--;for (int i = 1; i < m_index-1; i++)//最后一个为常数且倒数第二个次数为一，不需要打印{//两个if判断‘+’的输出if (m_indexarray[i] == 0){checkforindexarrayiszero++;tempindex--;continue;}if (m_indexarray[i] > 0)//严谨点来说这里似乎得考虑精度{//这个if是控制第一个数前面没有'+'if(checkforindexarrayiszero!=i)std::cout << '+';if (m_indexarray[i] != 1)std::cout << m_indexarray[i];std::cout << m_showtouser_character1 << m_showtouser_character2 << tempindex--;            }if (m_indexarray[i] < 0){if (m_indexarray[i] == -1)std::cout << '-' << m_showtouser_character1 << m_showtouser_character2 << tempindex--;elsestd::cout << m_indexarray[i] << m_showtouser_character1 << m_showtouser_character2 << tempindex--;}}tempindex += 1;while (tempindex--){if (m_indexarray[m_index - tempindex] == 0){checkforindexarrayiszero++;continue;}else if (m_indexarray[m_index - tempindex] > 0){  if (m_indexarray[m_index - tempindex] == 1){//tempindex==1是在判断是否是一次方，若是一次方则只需打印'+'if (tempindex == 1 && checkforindexarrayiszero != m_index-1)std::cout << '+' ;//下面两个if是对常数操作if (tempindex != 1 && checkforindexarrayiszero != m_index)std::cout << '+' << m_indexarray[m_index - tempindex];if (tempindex != 1 && checkforindexarrayiszero == m_index)std::cout << m_indexarray[m_index - tempindex];}else{//tempindex==1是在判断是否是一次方if (tempindex == 1 && checkforindexarrayiszero != m_index - 1)std::cout << '+' << m_indexarray[m_index - tempindex];//下面两个if是对常数操作if (tempindex != 1 && checkforindexarrayiszero != m_index)std::cout << '+' << m_indexarray[m_index - tempindex];if (tempindex != 1 && checkforindexarrayiszero == m_index)std::cout << m_indexarray[m_index - tempindex];}}else{if (m_indexarray[m_index - tempindex] == -1){if (tempindex == 1)std::cout << '-';elsestd::cout << m_indexarray[m_index - tempindex];}elsestd::cout << m_indexarray[m_index - tempindex];}      if (tempindex == 1)std::cout << 'x';}
}bool Poly::getarray()
{for (int i = 0; i <= m_index; i++)if (!(std::cin >> m_indexarray[i]))return false;return true;
}void Poly::getpointans(void)
{double* temp = new double[m_index + 1];unsigned long long tempindex=m_index;temp[0] = 1;for (int i = 0; i < m_index; i++){temp[i] *= m_point;m_ans += (temp[i] * m_indexarray[tempindex - 1 - i]);temp[i + 1] = temp[i];}m_ans += m_indexarray[m_index];std::cout << '\n' << m_ans << '\n';
}int main(void)
{std::cout<< "题目要求是输入一个多项式，那我就按照狭义理解不包括单独的常数项，最高次数输0也给你强制挂程序(\n\n"<< "后面所有不按要求输入都给你挂掉程序(\n"<< "首先输入带求解x的具体值\n";double point;if (!(std::cin >> point))return 0;std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');std::cout<< "输入第一个多项式的最高次数(若小数则强制向下取整,多个数输入强制取第一个):\n";long long index;if (!(std::cin >> index)||(index<=0))return 0;std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');Poly firstexpression(index, point);std::cout << "请输入每一项的系数(按照降幂依次输入，正数不需要输入+):\n";if (!firstexpression.getarray())return 0;std::cout << "\n这是你输入的第一个多项式:\n";firstexpression.showexpression();std::cout<< "\n如果没有显示，那恭喜你全部输入的0)\n";std::cout<< "\n输入第二个多项式的最高次数(若小数则强制向下取整，多个数输入强制取第一个):\n";std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');if (!(std::cin >> index)||(index<=0))return 0;std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');Poly secondexpression(index);std::cout << "请输入每一项的系数(按照降幂依次输入，正数不需要输入+):\n";if (!secondexpression.getarray())return 0;std::cout << "\n这是你输入的第二个多项式:\n";secondexpression.showexpression();std::cout << "\n如果没有显示，那恭喜你全部输入的0)\n";Poly ansexpression = firstexpression + secondexpression;std::cout << "\n这里是计算所得多项式结果：\n";std::cout << "多项式之和\n";ansexpression.showexpression();ansexpression.getpointans();std::cout << "多项式之差\n";ansexpression = firstexpression - secondexpression;ansexpression.showexpression();ansexpression.getpointans();std::cout<< "\n\n如果你发现什么式子都没输出，那就是两个多项式全部抵消完了\n"<< "下面是计算所得结果\n";system("pause");return 0;
}Poly operator+(const Poly& r1,const Poly& r2)
{unsigned long long maxindex = r1.m_index > r2.m_index ? r1.m_index : r2.m_index;unsigned long long minindex = r1.m_index < r2.m_index ? r1.m_index : r2.m_index;unsigned long long res = maxindex - minindex;Poly ans(maxindex,r1.m_point);if (r1.m_index > r2.m_index){for (unsigned long long i = 0; i < res; i++)ans.m_indexarray[i] = r1.m_indexarray[i];for (unsigned long long i = res; i <= maxindex; i++)ans.m_indexarray[i] = r1.m_indexarray[i] + r2.m_indexarray[i-res];}else{for (unsigned long long i = 0; i < res; i++)ans.m_indexarray[i] = r2.m_indexarray[i];for (unsigned long long i = res; i <= maxindex; i++)ans.m_indexarray[i] = r1.m_indexarray[i-res] + r2.m_indexarray[i];}return ans;
}Poly operator-(const Poly& r1, const Poly& r2)
{unsigned long long maxindex = r1.m_index > r2.m_index ? r1.m_index : r2.m_index;unsigned long long minindex = r1.m_index < r2.m_index ? r1.m_index : r2.m_index;unsigned long long res = maxindex - minindex;Poly ans(maxindex, r1.m_point);if (r1.m_index > r2.m_index){for (unsigned long long i = 0; i < res; i++)ans.m_indexarray[i] = r1.m_indexarray[i];for (unsigned long long i = res; i <= maxindex; i++)ans.m_indexarray[i] = r1.m_indexarray[i] - r2.m_indexarray[i - res];}else{for (unsigned long long i = 0; i < res; i++)ans.m_indexarray[i] = -r2.m_indexarray[i];for (unsigned long long i = res; i <= maxindex; i++)ans.m_indexarray[i] = r1.m_indexarray[i - res] - r2.m_indexarray[i];}return ans;
}