Question

factor completely.\\(15n^{2}+3n^{3}+4n+20\\)

Explanation:

Step1: Rearrange the terms

First, we rearrange the polynomial in descending order of the powers of \( n \):
\( 3n^{3}+15n^{2}+4n + 20 \)

Step2: Group the terms

We group the first two terms and the last two terms together:
\( (3n^{3}+15n^{2})+(4n + 20) \)

Step3: Factor out the GCF from each group

For the first group \( 3n^{3}+15n^{2} \), the greatest common factor (GCF) is \( 3n^{2} \). Factoring it out, we get:
\( 3n^{2}(n + 5) \)
For the second group \( 4n+20 \), the GCF is \( 4 \). Factoring it out, we get:
\( 4(n + 5) \)
So now our expression becomes:
\( 3n^{2}(n + 5)+4(n + 5) \)

Step4: Factor out the common binomial factor

We can see that both terms have a common binomial factor of \( (n + 5) \). Factoring that out, we get:
\( (n + 5)(3n^{2}+4) \)

Answer:

\( (n + 5)(3n^{2}+4) \)