Can x2 plus 1 be factored?

Answer 1

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)

Answer 2

No.