1. Roots (solutions) to a polynomial in a single variable

Quite why I was not taught this for ‘A’ level maths is beyond me (or more likely I was and have simply forgotten) but, if we have a polynomial in a single variable:

Then the general form of its factorisation is:

and it has the roots:

Here’s an (very) outline proof…

Take a polynomial with a known root then will divide evenly (no remainders) by and so we can say where is of one degree less than . We can continue this until we are left with a function of degree 0 – i.e. the constant (possibly 1) and then we have the form .

2 thoughts on “Learnt this week … 31 January 2014”

Regarding roots, in general some are complex. Perhaps that delayed coverage of polynomial factorization?

I just think I must have forgotten this. I even a year of maths at university (though it was more “maths recipes” than theory) and so I cannot believe we weren’t taught this.

Regarding roots, in general some are complex. Perhaps that delayed coverage of polynomial factorization?

I just think I must have forgotten this. I even a year of maths at university (though it was more “maths recipes” than theory) and so I cannot believe we weren’t taught this.