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To solve a polynomial equation I have written following program, is there any way to optimize this program.

Following code is working code:

Program takes input n,x where n is the deg of polynomial and x is the point at which the polynomial is to be evaluated.

   #include<stdio.h>

   int power(int x, int y);

   int main()
  {
  // n is the deg of polynomial
  // x is the value of polynomial for which it is to be evaluated
  int x=0,n=0,A[10],sum=0,i=0,M=0,y=0;

  printf("Enter value of n,x \n");
  scanf("%d %d",&n,&x);

  printf("Enter the coeficients\n");

  for(i=0;i<=n;i++)          //Taking coefiecent values
  {
     scanf("%d",&A[i]);
  }

  y=n;
  for(i=0;i<=n;i++)
  {
    M=power(x,y);
    sum=sum+(A[i]*M);
    y--;
   }

  printf("\nSum of polynomial is %d",sum);

  return 0;
 }


 int power(int x, int y)
 {
  int result = x;
  int i;
  if(y == 0) return 1;
  if(x < 0 || y < 0) return 0;

  for(i = 1; i < y; ++i)
  result *= x;

  return result;
}
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By following Horner's Method only n multiplications are needed.

#include <stdio.h>

int main()
{
   // n is the deg of polynomial
   // x is the value of polynomial for which it is to be evaluated
   int x=0,n=0,A[10],b,i;

   printf("Enter value of n,x \n");
   scanf("%d %d",&n,&x);

   //Taking coefficient values
   printf("Enter the coeficients\n");

   for(i=0;i<=n;i++) scanf("%d",&A[i]);

   for(i = n - 1,b = A[n];i >= 0;i--) b = b*x + A[i];

   printf("\nSum of polynomial is %d\n",b);

   return 0;
}
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If user enters the coefficients in A[n], A[n-1], ... A[1], A[0] order, code gets nice and tight. No need to save all the coefficients and no need to limit them to 10. Calculate the sum as you go.

BTW: Always good to check the results of scanf().

#include<stdio.h>

int main() {
  // n is the deg of polynomial
  // x is the value of polynomial for which it is to be evaluated
  int x, n, A;
  long sum = 0;  // or use long long

  printf("Enter value of n,x \n");
  if (scanf("%d %d", &n, &x) != 2) {
    return 1;  // bad input
  }

  printf("Enter the coefficients\n");  // spelling change
  while (n-- >= 0) {
    if (scanf("%d", &A) != 1) {
      return 1;  // bad input
    }
    sum *= x;
    sum += A;
  }
  printf("\nSum of polynomial is %ld", sum);
  return 0;
}
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