Question

Can anyone factorize the given term: x-a

Answer 1

`x-a` is a polynomial of degree 1, and as such it cannot be factorized.

In fact, when you factor a polynomial
`p(x)` of degree
`n`, you write it as

`p(x) = r(x)\cdot s(x),\quad \deg(r)=a,\quad \deg(s)=b,\quad a+b=n`

So, if a polynomial is already of degree one, you should write it as a product of two polynomials, whose degrees sum to 1.

So, the only option would be

`p(x) = r(x)\cdot s(x)`

with
`r(x)` of degree 1 and
`s(x)` of degree 0, i.e. a constant polynomial, i.e. a simple number.

But this factorization is trivial, because it only allows you to write expressions like

`x-a = 1\cdot(x-a),\qquad\text{or}\qquad 2\cdot(x-a)/(2)`

which are not actual polynomial factorizations.

Answer 2

factorize means to find the factors. what two terms can you multiply to get (x-a)?

The only thing I can come up with is the difference of squares which is: (√x + √a)(√x - √a)

Generally, we do not use square roots as factors so normally (x - a) would be considered as "prime" (cannot be factored).