Can this expression be factored?
4x^2+9
My homework assignment says to factor completely and this is one of the problems but I don't think this expression can be factored. Am I wrong? If so how do I factor it.
I can not factor that
are you sure it is not
4 x^2 - 9
that would be the difference of squares which is
(2 x - 3)(2 x + 3)
You are correct in thinking that the expression 4x^2 + 9 cannot be factored in terms of real numbers. This is known as a prime polynomial, meaning it cannot be factored any further within the set of real numbers.
However, if you allow for complex numbers, the expression can be factored using complex numbers. In this case, the factorization of 4x^2 + 9 can be written as:
(2xi + 3)(-2xi + 3)
Here, the constant term 9 is factored into two complex conjugates, 2xi + 3 and -2xi + 3, where xi represents the imaginary unit.
So, to summarize, 4x^2 + 9 cannot be factored within the set of real numbers, but it can be factored into complex conjugate factors.