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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 $9$ : $1, 3, 9$ $\newline$ Common factors of the coefficients: $3$ $\newline$ Both terms have at least $p^2$ in common. $\newline$ Therefore, the GCF is $3p^2$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For $6p^3$ , we divide by $3p^2$ to get $2p$ . $\newline$ For $9p^2$ , we divide by $3p^2$ to get $3$ .
Write Original Polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $6p^3 + 9p^2 = 3p^2(2p) + 3p^2(3)$ $\newline$ Combining the terms inside the parentheses, we get: $\newline$ $6p^3 + 9p^2 = 3p^2(2p + 3)$

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