C++でArrayを使って多項式の計算

c＋＋でArrayを使って多項式の計算（足し算と掛け算）をするプログラムを書いています。

＜期待する結果＞
例えば：
多項式a＝４＋２xー４x＾２ー６x＾３
多項式b＝３−２x＋４x＾２＋６x＾３
であった時に、これら２つの式を足した結果と掛けた結果を表示させたいです。

＜自分が書いたコード＞

c++
1#include <iostream>
2#include <cmath>
3using namespace std;
4
5struct Poly{
6	int degree;
7	int* coeffs;
8};
9
10//function prototype
11Poly* readPoly();
12void outputPoly(const Poly* p, char x);
13Poly* addPoly(const Poly* a, const Poly* b);
14Poly* multPoly(const Poly* a, const Poly* b);
15void deletePoly(Poly* &p);
16
17int main(){
18
19	//ask user to enter a polynominal and call function for reading
20	cout<<"Enter a polynominal: "<<endl;
21	Poly* a = readPoly();
22
23	//ask user to enter another polynominal and call function for reading
24	cout<<"Enter another polynominal: "<<endl;
25	Poly* b = readPoly();
26
27	//print first polynominal
28	cout<<"a=";
29	outputPoly(a,'x');
30	cout<<endl;
31
32	//print second polynominal
33	cout<<"b=";
34	outputPoly(b,'x');
35	cout<<endl;
36
37	//print result for addition
38	Poly* ad = addPoly(a,b);
39	cout<<"addition: ";
40	outputPoly(ad,'x');
41	cout<<endl;
42
43	//print result for multiplication
44	Poly* m = multPoly(a,b);
45	cout<<"multiply: ";
46	outputPoly(m,'x');
47	cout<<endl;
48
49	return 0;
50}
51
52Poly* readPoly(){
53	int deg;
54	int* coefficient;
55
56	//ask user to enter a degree
57	cout<<"Degree: "<<endl;;
58	cin>>deg;
59
60	//create array
61	coefficient = new int[deg+1];
62
63	//fill array
64	cout<<"Coefficients: "<<endl;
65	for(int i=0; i<=deg; i++){
66		cin>>coefficient[i];
67	}
68
69	Poly* p;
70	p = new Poly;
71	p->degree = deg;
72	p->coeffs = coefficient;
73
74	return p;
75}
76
77void outputPoly(const Poly* p, char x){
78
79	//print polynominals
80	for(int i=1; i<=p->degree; i++){
81		//when coefficient is zero
82		if(p->coeffs[i]==0)
83			cout<<p->coeffs[i];
84		//when coefficient is positive num, add plus sign
85		else if(p->coeffs[i]>0)
86			cout<<"+"<<p->coeffs[i]<<"*"<<x<<"^"<<i;
87		//when coefficient is negative num, add minus sign
88		else if(p->coeffs[i]<0)
89			cout<<"-"<<p->coeffs[i]<<"*"<<x<<"^"<<i;
90		//when coefficient is 1
91		else if(p->coeffs[i]==1)
92			cout<<"+"<<x<<"^"<<i;
93			//any other cases
94			else
95				cout<< *(p->coeffs);
96		}
97}
98
99Poly* addPoly(const Poly* a, const Poly* b){
100
101
102}
103
104Poly* multPoly(const Poly* a, const Poly* b){
105	int i,j;
106	i=0;
107	j=0;
108
109	if(a==0)
110		return b;
111	else if(b==0)
112		return a;
113
114	Poly* res;
115	res = new Poly;
116	res->degree = a->degree+b->degree;
117
118	int* c = new int[res->degree-1];
119
120	while(i!=res->degree){
121		while(j!=res->degree)
122			c[i+j]+=a->c[i]*b->c[j];
123		i++;
124		j++;
125	}
126
127	res->coeffs = c;
128
129	return res;
130}
131
132void deletePoly(Poly* &p){
133	delete[]p->coeffs;
134	delete p;
135	p=NULL;
136}
137

＜問題点＞
１）肝心のaddPolyとmultPolyのところをどう書いたら良いかそもそもわからず困っています。
２）自分でmultPolyを途中まで書いてみたのですが、多項式aもしくはbが０であった場合に０でない方の多項式を戻り値としたいのですが、if文でreturn aとreturn bと書いたところエラーが表示されどう直せば良いかわかりません。

c++
1Poly* multPoly(const Poly* a, const Poly* b){
2	int i,j;
3	i=0;
4	j=0;
5
6	if(a==0)
7		return b;
8	else if(b==0)
9		return a;
10
11	Poly* res;
12	res = new Poly;
13	res->degree = a->degree+b->degree;
14
15	int* c = new int[res->degree-1];
16
17	while(i!=res->degree){
18		while(j!=res->degree)
19			c[i+j]+=a->c[i]*b->c[j];
20		i++;
21		j++;
22	}
23
24	res->coeffs = c;
25
26	return res;
27
28}