Language in Math class- Factorisation

One of my favourite topic is language in Math class. many times I feel language and Math can be a same subject and not separate subjects. The word factorisation is heard a lot in Math class from primary classes to high school when we deal with simple numbers to solving a quadratic equation.

I ask my students what is factorisation. More often I don't get an answer to it, instead they try to share some examples(problems) they did before. But I rarely hear a full sentence simple definition to it. If you are a teacher or a parent working with your child on math, ask this question yourself. Do you have any answer? If yes, what it is.

In my experience, having the knowledge of what is factorisation and able to express it in any language have a huge impact on students' ability to work with this idea. Many times our math curriculum and syllabus just fall into the trap of mere methods and steps to solve some 'typical problems' and not paying any attention to 'meaning making' or 'seeing the beauty in Math'

Factorisation is nothing but expressing a number as a product of two or more other numbers( or simply 'factors'). I feel meaning making starts from such definitions and unpacking of it.

As a teacher what you think about it? Does language of Math class has an impact on how the students are progressing in their studies? or it doesn't matter at all?