Question

factor out the greatest common factor. if the greatest common factor is 1, just retype the polynomial.
$8p^{7} + 24p^{4} - 16p^{2}$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 8, 24, -16.
Factors of 8: 1, 2, 4, 8
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 16: 1, 2, 4, 8, 16
GCF of 8, 24, 16 is 8.

Step2: Find GCF of variables

For \( p^7 \), \( p^4 \), \( p^2 \), the lowest power of \( p \) is \( p^2 \).

Step3: Factor out GCF

Factor out \( 8p^2 \) from each term:
\( 8p^7 + 24p^4 - 16p^2 = 8p^2(p^5 + 3p^2 - 2) \)

Answer:

\( 8p^2(p^5 + 3p^2 - 2) \)