Factor 4x^2+9

Problem

4*x2+9

Solution

1. Identify the form of the expression. The expression 4*x2+9 is a sum of two squares because it can be written as (2*x)2+(3)2

2. Apply the complex factorization rule. A sum of squares a2+b2 does not factor over the set of real numbers, but it factors over the set of complex numbers using the identity a2+b2=(a+b*i)*(a−b*i)

3. Substitute the values a=2*x and b=3 into the complex factorization formula.

4. Write the final factored form using the imaginary unit i

Final Answer

4*x2+9=(2*x+3*i)*(2*x−3*i)

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