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

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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

6r^3 + 9r

Find GCF Factors: We need to find the greatest common factor (GCF) of the terms $6r^3$ and $9r$ . To do this, we will list the factors of the coefficients and the powers of $r$ to find the common factors. $\newline$ Factors of $6$ : $1, 2, 3, 6$ $\newline$ Factors of $9$ : $1, 3, 9$ $\newline$ Common factors of the coefficients: $3$ $\newline$ Powers of $r$ : $r^3$ and $r$ $\newline$ The smallest power of $r$ that is common to both terms is $r$ . $\newline$ Therefore, the GCF of $6r^3$ and $9r$ is $9r$ $5$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For $6r^3$ , we divide by $3r$ to get $2r^2$ . $\newline$ For $9r$ , we divide by $3r$ to get $3$ .
Write Original Polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $6r^3 + 9r = 3r(2r^2 + 3)$

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