Question

Explain why the expression `13x+10` cannot be factored?

Answer 1

There are no common factors between the two terms `color(red)(13x)` and `color(blue)(10)` - see explanation below.

Explanation:

First, we can try factoring the constants in each term:

13 is a prime number and therefore can only be factored to 1 and 13.

10 can be factored as (1 x 10) or (2 x 5).

Because there are no common factors other than `1` the constants cannot be factored.

And, because there is no `x` in the second term (10), we cannot factor an `x` out of the two terms.

Therefore this expression cannot be factored.