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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $6p^3 - 9p^2$

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Factor out a monomial

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Q. Factor out the greatest common factor. If the greatest common factor is

1

, just retype the polynomial.

\newline

6p^3 - 9p^2

Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms $6p^3$ and $9p^2$ . To do this, we will list the factors of the coefficients and the powers of $p$ to find the highest common factor. $\newline$ Factors of $6$ : $1$ , $2$ , $3$ , $6$ $\newline$ Factors of $9$ : $1$ , $3$ , $9$ $\newline$ The common factors of the coefficients are $1$ and $3$ . The highest common factor is $3$ . $\newline$ Both terms have a $9p^2$ $5$ in common. $\newline$ Therefore, the GCF of $6p^3$ and $9p^2$ is $9p^2$ $8$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For the first term, $6p^3$ divided by $3p^2$ gives us $2p$ . $\newline$ For the second term, $9p^2$ divided by $3p^2$ gives us $3$ .
Write Original Polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $6p^3 - 9p^2 = 3p^2(2p) - 3p^2(3)$ $\newline$ This simplifies to $3p^2(2p - 3)$ .

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