Expression: 30p⁷-10p⁴+6p

Question

GCF: □
Factored form: □

Answer 1

To factor the expression $30p^7-10p^4+6p$, we start by finding the greatest common factor (GCF) of the terms.

1. Identify coefficients:

   • The coefficients are 30, -10, and 6.
   • The GCF of these coefficients is 2.

2. Identify the variable part:

   • The variable terms are $p^7$, $p^4$, and $p^1$.
   • The smallest power of $p$ is $p^1$.

3. Combine the GCF:

   • The GCF of the entire expression is $2p$.

Now, we can factor $2p$ out of each term:

$$30p^7-10p^4+6p=2p(15p^6-5p^3+3)$$

Thus, we can fill in the blanks:

• GCF: $2p$
• Factored form: $2p(15p^6-5p^3+3)$