NO!!!
x^2 + 1 = x^2 + 1^2 . This does NOT factor!!!!!
Remember , two squared terms with a positive between them, does NOT factor. However, two squared terms with a negative between them does factor.
e.g.
x^2 - 1^2 = ( x + 1)(x - 1) Note the change of signs inside the brackets.
So taking the Pythagorean equation ; a^2 + b^2 = c^2,, this does NOT factor. However, algebraically rearranging we have a^2 = c^2 - b^2 does factor to
a^2 = (c - b)(c + b)
That expression can not be factored.
It is: (x+1)(x+12) when factored
x3 - x2 + 2x = x*(x2 - x + 2) which cannot be factored further.
It is a quadratic expression and when factored is: (x+1)(x+1)
x2+x-6 = (x-2)(x+3) when factored
It is (x-1)(x-1) when factored
x2 + 1 can't be factored in the real numbers. If complex numbers are acceptable, it can be factored as (x + i)(x - i).
That expression can not be factored.
It is: (x+1)(x+12) when factored
x2 + 6x + 5 can be factored into (x+1) (x+5)
x3 - x2 + 2x = x*(x2 - x + 2) which cannot be factored further.
It is a quadratic expression and when factored is: (x+1)(x+1)
x2+x-6 = (x-2)(x+3) when factored
x2+6x-7 = (x+7)(x-1) when factored
It is: (x+1)(x+6) when factored
x2 + 5xy - 18y2 can not be factored.
x2 + 5x - 120 can not be factored.