Factor the polynomial by grouping.
$3p^3-30-5p^2+18p=$  

To factor the polynomial $ 3p^3 - 30 - 5p^2 + 18p $ by grouping, follow these steps:

1. **Rearrange the terms** to group them in pairs:
   \[
   3p^3 - 5p^2 + 18p - 30
   \]

2. **Factor out the greatest common factor** (GCF) from each group:
   \[
   p^2(3p - 5) + 6(3p - 5)
   \]

3. Notice that both groups have a common factor of $ (3p - 5) $. Factor this out:
   \[
   (3p - 5)(p^2 + 6)
   \]

So, the factored form of the polynomial is:
\[
\boxed{(3p - 5)(p^2 + 6)}
\]

Would you like details or have any questions?

Here are some related questions to consider:
1. How do you factor a polynomial that doesn't group easily?
2. What is the importance of recognizing common factors when factoring?
3. How can you verify that a polynomial is factored correctly?
4. How do you handle polynomials with four terms in different orders?
5. What methods can be used if grouping doesn't initially work?

**Tip:** Always check your final factors by expanding them to see if you get the original polynomial.

Factor the polynomial by grouping. 3p^3 - 30 - 5p^2 + 18p =

Learn how to factor the polynomial 3p^3 - 30 - 5p^2 + 18p using the grouping method. This detailed solution covers key algebraic concepts such as factoring by grouping, recognizing the greatest common factor (GCF), and applying the distributive property. Suitable for students in Grades 9-11.

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