Answered

IDNLearn.com is your go-to resource for finding precise and accurate answers. Discover reliable and timely information on any topic from our network of knowledgeable professionals.

Factor the following polynomial completely using the greatest common factor. If the expression cannot be factored, enter the expression as is.

[tex]\[ 6y + 48 \][/tex]

Sagot :

GinnyAnsweridn
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.
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.