Find the Equivalent Expression: Simplifying 15z²+50zx

Choose the expression that is equivalent to the following:

$15z^2+50zx$

To solve the problem, the goal is to factor the expression $15z^2 + 50zx$ by finding the greatest common factor.

Step 1: Identify the greatest common factor (GCF):

• The terms in the expression are $15z^2$ and $50zx$.
• The numerical coefficients are $15$ and $50$, and their GCF is $5$.
• Both terms contain $z$ as a factor, so $z$ is also part of the GCF.
• Therefore, the GCF of both terms is $5z$.

Step 2: Factor the expression using the GCF:

• Divide each term by the GCF $5z$:
• $\frac{15z^2}{5z} = 3z$
• $\frac{50zx}{5z} = 10x$
• Thus, the expression can be rewritten as the product of the GCF and the remaining terms: $5z(3z + 10x)$.

Therefore, the expression $15z^2 + 50zx$ is equivalent to $5z(3z + 10x)$.