Prime and non prime quadratic expressions

The concept of 'prime' and 'non prime' is the same in algebra as it is in the number theory

Prime quadratic expressions

Prime numbers are defined as numbers which cannot be factored. Similarly, prime quadratic expressions are those algebraic expressions that cannot be factored. 

Examples of prime quadratic expressions:

`x^2 + 2x + 2`
`6x^2 - 7x + 18`
`x^2 - 7x + 18`
`2x^2 + 11x + 18`

Non prime quadratic expressions

Non prime numbers are defined as the numbers that have factors other than 1 and themselves; implying that there are numbers other than 1 and itself that are able to divide the given number without getting any remainder left. Similarly in algebra, non prime quadratic expressions are those algebraic expressions that possess linear or smaller degree factors. These factors are linear algebraic expressions, and divide the given quadratic expression without leaving any remainder. 

Examples of non prime quadratic expressions:

`x^2 + 5x - 6` is a non prime quadratic expression since it has the factors (x - 1) and (x + 6)

`x^2 - 5x + 6` is a non prime quadratic expression since it has the factors (x - 3) and (x - 2)
`x^2 - 9x + 20` is a non prime quadratic expression since it has the factors (x - 5) and (x - 4)