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

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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

9b^2 - 6b

Identify Factors: We need to find the greatest common factor (GCF) of the terms $9b^2$ and $6b$ . To do this, we will list the factors of the coefficients and the variables separately and then identify the common factors. $\newline$ Factors of $9$ : $1$ , $3$ , $9$ $\newline$ Factors of $6$ : $1$ , $2$ , $3$ , $6$ $\newline$ The common factor for the coefficients is $3$ . $\newline$ For the variables, since both terms have at least one ' $6b$ $2$ ', the common factor will include ' $6b$ $2$ '.
Express as Product: Now we will express each term as a product of the GCF and the remaining factors. $\newline$ For $9b^2$ , we can write it as $3 \times 3 \times b \times b$ . $\newline$ For $6b$ , we can write it as $3 \times 2 \times b$ . $\newline$ The GCF of $9b^2$ and $6b$ is $3b$ .
Factor Out GCF: We will now factor out the GCF from each term. $\newline$ $9b^2$ can be written as $3b \times 3b$ . $\newline$ $6b$ can be written as $3b \times 2$ . $\newline$ So, the polynomial $9b^2 - 6b$ can be factored as: $\newline$ $9b^2 - 6b = 3b(3b - 2)$ .

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