Matlab's factor() function

Let's talk about the factor() function in Matlab. It's a useful tool for algebraic expression factoring.

factor(x)

When you have an algebraic expression that you want to simplify or manipulate, factoring can help you break it down into simpler factors. That's where the factor() function comes in handy.

This symbolic computation function returns the same expression in factored form.

What does factoring an algebraic expression mean? Factoring an algebraic expression involves breaking down an expression into a product of simpler factors. This process can be useful for simplifying the expression and making it easier to manipulate or solve. For example, the factoring of the expression $$ x^2 + 2x + 1 = (x + 1)^2 = (x+1) \cdot (x+1) $$ In this way, the original expression is transformed into a simpler and more understandable form. At a glance, you can understand when the expression is zero.

So, how do we use the factor() function in Matlab?

It's quite simple, really. First, you need to define your algebraic expression as a symbolic variable using the syms() function.

Once you've done that, you can then input your expression as an argument into the factor() function and it will return the same expression in a factored form.

Let me give you an example.

Consider the following algebraic expression:

$$ x^2 + 4x +3 $$

E' un polinomio di 2° grado con una variabile incognita (x)

We can define x as a symbolic variable using syms x like this

>> syms x

Then, we can define our algebraic expression as y=x^2+4*x+3

>> y=x^2+4*x+3

Finally, we can use the factor(y) function to factor our expression.

>> factor(y)

The result of the factoring operation will be an array of factors, which in this case is [x+3, x+1].

ans =
[x + 3, x + 1]

Therefore, the factored form of the expression is:

$$ (x+3) \cdot (x+1) $$

In factored form, it's easier to find the zeros, that is, the points where the polynomial is zero.

In this case, the zeros of the polynomial are x=-3 and x=-1.

Note. According to the zero product property, it's sufficient for one of the factors to be zero to have a zero product. If x=-3, the first factor (x+2) becomes zero. If x=-1, the second factor (x+1) becomes zero. In both cases, the expression (x+3)(x+1) equals zero because the product is zero.

And there you have it. The factor() function in Matlab is a powerful tool for algebraic expression factoring, and with a little practice, you'll be factoring expressions like a pro in no time.