December 3, 2023
/ 393 /# How to Multiply Two Polynomials in MATLAB?

**Polynomial Multiplication: A Review**

**How to use MATLAB **

### Syntax of the function:

### Arguments of the conv() function:

### Return Value of the conv() function:

**An Example Problem:**

### Explanation of the MATLAB Code:

**Wrap Up**

Polynomial multiplication is a fundamental operation in algebra, and MATLAB provides a powerful tool to perform this operation efficiently.

In this article, we will look at how to multiply two polynomials using MATLAB, by using the function: `conv()`

.

Before looking into how to use MATLAB to multiply polynomials together, letโs briefly review polynomial multiplication.

Given two polynomials:

$ P(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1x + a_0 $

$Q(x) = b_m x^m + b_{m-1} x^{m-1} + \ldots + b_1 x + b_0$

The product of $P(x)$ and $Q(x)$, denoted as $ P(x) \cdot Q(x) $, is calculated by multiplying each term of the first polynomial by each term of the second polynomial and summing the results.

In mathematical terms, the product is:

$P(x) \cdot Q(x) = \sum_{i=0}^{n} \sum_{j=0}^{m} a_i b_j x^{i+j}$

`conv()`

Function to Multiply Polynomials?MATLAB simplifies the process of polynomial multiplication with the `conv()`

function.

This function operates on two vectors, representing the coefficients of the polynomials, and returns the coefficients of their product.

```
conv(p1, p2)
```

The โ**conv()**โ function takes two parameters; which are vectors that hold the coefficient of each polynomial.

`p1`

: Represents the coefficient vector of the first polynomial.`p2`

: Represents the coefficient vector of the second polynomial.

The result is a coefficient vector representing the product polynomial.

Letโs consider the following polynomials:

$P(x) = 1x^2 + 2x + 3 $

$Q(x) = 4x^2 + 5x + 6 $

If you want to multiply these two polynomials together, the MATLAB code is:

```
% Define the coefficients of the first polynomial
p1 = [1, 2, 3];
% Define the coefficients of the second polynomial
p2 = [4, 5, 6];
% Multiply the polynomials using conv()
product = conv(p1, p2);
% Display the product polynomial
disp(product);
```

The result of this code is the coefficient vector `[4, 13, 28, 27, 18]`

, representing the product polynomial:

Result: $ 4x^4 + 13x^3 + 28x^2 + 27x + 18$

Firstly, the polynomial $P(x) = 1x^2 + 2x + 3$ is represented as a vector by extracting its coefficients.

This vector is stored in a variable named `p1`

. In MATLAB syntax, it is defined as:

```
p1 = [1, 2, 3];
```

Similarly, the coefficients of the second polynomial $Q(x) = 4x^2 + 5x + 6$ are stored in another variable named `p2`

:

```
p2 = [4, 5, 6];
```

Now, the convolution function `conv()`

is used to multiply the two polynomials represented by the vectors `p1`

and `p2`

.

The result is stored in a variable called `product`

:

```
product = conv(p1, p2);
```

At this point, the `product`

variable holds the coefficients of the product polynomial.

Finally, the `disp()`

function is used to display the result on the screen:

```
disp(product);
```

The displayed result is the coefficient vector `[4, 13, 28, 27, 18]`

, which corresponds to the product polynomial:

$ 4x^4 + 13x^3 + 28x^2 + 27x + 18 $

As a wrap up, to multiply polynomials in MATLAB using the `conv()`

function, you start by defining coefficient vectors for each polynomial.

The `conv()`

function then efficiently computes the product of the polynomials by convolving their coefficient vectors.