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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $6x^3 - 10x^2$

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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

6x^3 - 10x^2

Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms $6x^3$ and $10x^2$ . To do this, we will first list the factors of the coefficients and the powers of $x$ . $\newline$ Factors of $6$ : $1$ , $2$ , $3$ , $6$ $\newline$ Factors of $10$ : $1$ , $2$ , $10x^2$ $1$ , $10$ $\newline$ The common factors of the coefficients are $1$ and $2$ . $\newline$ Since both terms have at least an $10x^2$ $5$ , we can factor out $10x^2$ $5$ as well. $\newline$ The GCF of $6x^3$ and $10x^2$ is therefore $10x^2$ $9$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For $6x^3$ , we divide by $2x^2$ to get $3x$ . $\newline$ For $10x^2$ , we divide by $2x^2$ to get $5$ .
Write Original Polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $6x^3 - 10x^2 = 2x^2(3x - 5)$

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