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

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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

6z^3 - 9z^2

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms $6z^3$ and $9z^2$ . The GCF is the highest number and the highest power of $z$ that divides both terms without a remainder. $\newline$ The factors of $6$ are $1$ , $2$ , $3$ , and $6$ . The factors of $9$ are $1$ , $3$ , and $9$ . The common factors are $3$ . $\newline$ Both terms also have a $9z^2$ $3$ term in common. $\newline$ Therefore, the GCF is $9z^2$ $4$ .
Find common factors: Divide each term by the GCF to find the remaining factors. $\newline$ For $6z^3$ , divide by $3z^2$ to get $2z$ . $\newline$ For $9z^2$ , divide by $3z^2$ to get $3$ .
Divide terms by GCF: Write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $6z^3 - 9z^2 = 3z^2(2z) - 3z^2(3)$ $\newline$ Combine the terms inside the parentheses. $\newline$ $6z^3 - 9z^2 = 3z^2(2z - 3)$

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