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

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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

9w^3 + 6w^2

Find GCF of terms: We need to find the greatest common factor (GCF) of the terms $9w^3$ and $6w^2$ . To do this, we will list the factors of the coefficients and the powers of $w$ . $\newline$ 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 part, since both terms have at least $6w^2$ $4$ , we can factor out $6w^2$ $4$ . $\newline$ The GCF of $9w^3$ and $6w^2$ is therefore $6w^2$ $8$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For $9w^3$ , we divide by $3w^2$ to get $3w$ . $\newline$ For $6w^2$ , we divide by $3w^2$ to get $2$ .
Write original polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $9w^3 + 6w^2 = 3w^2(3w) + 3w^2(2)$ $\newline$ Combining the terms inside the parentheses, we get: $\newline$ $9w^3 + 6w^2 = 3w^2(3w + 2)$

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