To factor the given expression [tex]\( 15n^2 - 6n \)[/tex], we will follow these steps:
1. Identify the greatest common factor (GCF):
The coefficients of the terms are 15 and 6. The GCF of 15 and 6 is 3. Both terms also contain the variable [tex]\( n \)[/tex]. The smallest power of [tex]\( n \)[/tex] in the terms is [tex]\( n^1 \)[/tex], so the GCF is [tex]\( 3n \)[/tex].
2. Factor out the GCF from each term:
We factor [tex]\( 3n \)[/tex] out of each term in the expression:
[tex]\[
15n^2 - 6n = 3n \cdot 5n - 3n \cdot 2
\][/tex]
3. Write the expression as a product:
After factoring out [tex]\( 3n \)[/tex], we have:
[tex]\[
15n^2 - 6n = 3n (5n - 2)
\][/tex]
Therefore, the factored form of the given expression [tex]\( 15n^2 - 6n \)[/tex] is:
[tex]\[
3n (5n - 2)
\][/tex]
