Final answer:
The GCF of 15x² and 30x is 15x. Factoring out the GCF from 15x² + 30x gives 15x(x + 2), which confirms our GCF is correct and simplifies the original equation.
Step-by-step explanation:
The greatest common factor, or GCF, of the expressions 15x² and 30x is what we are looking for to simplify the given equation 15x² + 30x = GCF * (x + 2). To determine the GCF of 15x² and 30x, we need to consider both the coefficients and the variables. The coefficients 15 and 30 share a common factor of 15, and the variable part x is present in both terms with the least power being x¹ in 30x.
Therefore, the GCF of 15x² and 30x is 15x. When we factor out the GCF from the left side of the equation, we get: 15x² + 30x = 15x(x + 2), which matches the original equation. Consequently, the equation simplifies to 15x(x + 2) = 15x * (x + 2) and confirms our GCF is correct.