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

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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

9p^2 - 6p

Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms $9p^2$ and $6p$ . To do this, we will list the factors of the coefficients and the powers of $p$ to find the common factors. $\newline$ Factors of $9$ : $1$ , $3$ , $9$ $\newline$ Factors of $6$ : $1$ , $2$ , $3$ , $6$ $\newline$ The common factors of the coefficients are $1$ and $3$ . $\newline$ For the variable $p$ , since the smallest power of $p$ is $1$ (in the term $6p$ ), the GCF will include $p$ to the first power. $\newline$ The GCF of $9p^2$ and $6p$ is $p$ $1$ .
Divide by GCF: Now we will divide each term by the GCF to factor it out. $\newline$ For the term $9p^2$ , we divide by $3p$ to get $3p$ . $\newline$ $9p^2 \div 3p = 3p$ $\newline$ For the term $6p$ , we divide by $3p$ to get $2$ . $\newline$ $6p \div 3p = 2$
Write Factored Form: We can now write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $9p^2 - 6p = 3p(3p - 2)$ $\newline$ This is the factored form of the polynomial.

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