**This method is used to find the value of a polynomial of degree n for a given value of x**. In general, a polynomial is solved by solving all terms one by one and then calculating the sum of all terms.

__DERIVATION__

A given polynomial is of the form

**(They may be positive or negative) and n is a positive integer.**

Now the value of this polynomial is to be found for a given x.

The idea of this method is to initialize the result as the coefficient of ${\mathrm{x}}^{\mathrm{n}}$, then multiplying this result with x, and then add the next coefficient to the result. Finally, the result will be calculated by repeating this procedure.

__INPUT:__

A polynomial of degree n

__OUTPUT:__

The value of the polynomial for a given x.

__PROCESS:__

```
Step 1: [taking the inputs from the user]
Read n [the number of terms of the polynomials]
for i = 0 to n - 1 repeat
Read arr[i] [the co-efficient of the polynomials]
[End of ‘for’ loop]
Read x [the value for which the value of the polynomial is to be calculated]
Step 2: [Horner’s Method]
Set r ← arr[0]
for i = 1 to n - 1 repeat
Set r ← r × x + arr[i]
Print r
[End of Horner’s method]
```

__ADVANTAGES__

**1.** It reduces the number of multiplication operations.

**2.** Time complexity is reduced from the normal process of evaluation.

__DISADVANTAGES__

**1.** All the operations are dependent. The next calculation is dependent on the previous data, so, parallelism cannot be achieved for this algorithm.

__APPLICATIONS__

**1.** This method is used to find the value of a polynomial more efficiently and in less time.

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