Question

factor $6y^2 + 15y$.

Explanation:

Step1: Find the GCF of coefficients and variables

First, find the greatest common factor (GCF) of the coefficients 6 and 15, and the common variable part. The GCF of 6 and 15 is 3, and the common variable part is \( y \) (since \( y^2 = y\times y \) and \( y = y\times1 \), the lowest power of \( y \) is \( y \)). So the GCF is \( 3y \).

Step2: Factor out the GCF

Factor out \( 3y \) from each term in \( 6y^2 + 15y \).
For the first term \( 6y^2 \), dividing by \( 3y \) gives \( \frac{6y^2}{3y}=2y \).
For the second term \( 15y \), dividing by \( 3y \) gives \( \frac{15y}{3y}=5 \).
So, \( 6y^2 + 15y = 3y(2y + 5) \).

Answer:

\( 3y(2y + 5) \)