Certainly! Let's factor the polynomial [tex]\( 6y + 48 \)[/tex] completely using the greatest common factor (GCF).
### Step-by-Step Solution:
1. Find the Greatest Common Factor (GCF):
- First, identify the GCF of the coefficients of the terms in the polynomial.
- The coefficients here are [tex]\( 6 \)[/tex] (from [tex]\( 6y \)[/tex]) and [tex]\( 48 \)[/tex].
- The GCF of [tex]\( 6 \)[/tex] and [tex]\( 48 \)[/tex] is [tex]\( 6 \)[/tex].
2. Factor Out the GCF:
- Next, factor out [tex]\( 6 \)[/tex] from each term in the polynomial.
- Express [tex]\( 6y + 48 \)[/tex] by pulling out the GCF (which is [tex]\( 6 \)[/tex]):
[tex]\[
6y + 48 = 6(y + 8)
\][/tex]
- Here, [tex]\( 6y \)[/tex] divided by [tex]\( 6 \)[/tex] gives [tex]\( y \)[/tex], and [tex]\( 48 \)[/tex] divided by [tex]\( 6 \)[/tex] gives [tex]\( 8 \)[/tex].
3. Combine Terms:
- Once we have factored out the GCF, the polynomial in its factored form is:
[tex]\[
6(y + 8)
\][/tex]
### Final Answer:
The polynomial [tex]\( 6y + 48 \)[/tex] is completely factored as:
[tex]\[
6(y + 8)
\][/tex]
This is the most simplified form using the GCF.
