Question

Why can't we factorize x^2+49

Answer 1

Technically, we can factorize it, but then we have to use imaginary number.

See, we know that \(a^2-b^2 = (a+b)(a-b)\), right? Let \(b=ci\), we have \[a^2-(ci)^2 = a^2-i^2c^2 = a^2-(-1)c^2 = a^2+c^2\]

So factoring it would get you \((a+ci)(a-ci)\)

Answer 2

@sanjii06 Does that make sense? You have learned imaginary number, right?