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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $4n^3 + 8n^2$

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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

4n^3 + 8n^2

Find GCF of terms: We need to find the greatest common factor (GCF) of the terms $4n^3$ and $8n^2$ . To do this, we will list the factors of the coefficients and the powers of $n$ . $\newline$ Factors of $4$ : $1$ , $2$ , $4$ $\newline$ Factors of $8$ : $1$ , $2$ , $4$ , $8$ $\newline$ Common factors of the coefficients: $1$ , $2$ , $4$ $\newline$ Since both terms have at least an $8n^2$ $5$ , we can include $8n^2$ $5$ in the GCF. $\newline$ GCF of $4n^3$ and $8n^2$ : $8n^2$ $9$
Express terms as product: Now we will express each term as a product of the GCF and the remaining factors. $\newline$ $4n^3$ can be written as $4n^2 \times n$ . $\newline$ $8n^2$ can be written as $4n^2 \times 2$ .
Factor out GCF from polynomial: We can now factor out the GCF from the polynomial. $\newline$ $4n^3 + 8n^2$ $\newline$ = $4n^2 \cdot n + 4n^2 \cdot 2$ $\newline$ = $4n^2(n + 2)$

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