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

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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

2n^3 - 6n^2

Identify GCF of Terms: Identify the greatest common factor (GCF) of the terms $2n^3$ and $6n^2$ . The GCF is the highest number and the highest power of $n$ that divides both terms. $\newline$ For the coefficients, the GCF of $2$ and $6$ is $2$ . $\newline$ For the powers of $n$ , since both terms have at least an $n^2$ , the GCF includes $n^2$ . $\newline$ Therefore, the GCF of $2n^3$ and $6n^2$ is $6n^2$ $1$ .
Divide by GCF: Divide each term by the GCF to find the remaining factors. $\newline$ For the first term, $2n^3$ divided by $2n^2$ is $n$ . $\newline$ For the second term, $6n^2$ divided by $2n^2$ is $3$ .
Write Factored Form: Write the original polynomial as the product of the GCF and the remaining factors. $\newline$ The factored form of the polynomial is $2n^2(n - 3)$ .

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