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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $10z^3 - 8z^2$

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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

10z^3 - 8z^2

Find GCF Factors: We need to find the greatest common factor (GCF) of the terms $10z^3$ and $8z^2$ . To do this, we will list the factors of the coefficients and the powers of $z$ . $\newline$ Factors of $10$ : $1$ , $2$ , $5$ , $10$ $\newline$ Factors of $8$ : $1$ , $2$ , $8z^2$ $1$ , $8$ $\newline$ The common factors of the coefficients are $1$ and $2$ . $\newline$ For the variable $z$ , since both terms have at least $8z^2$ $6$ , we can take $8z^2$ $6$ as a common factor. $\newline$ The GCF of $10z^3$ and $8z^2$ is therefore $z$ $0$ .
Identify Common Factors: Now we will divide each term by the GCF to factor it out. $\newline$ For the first term, $10z^3$ divided by $2z^2$ is $5z$ . $\newline$ For the second term, $8z^2$ divided by $2z^2$ is $4$ . $\newline$ So, the polynomial factored by the GCF is $2z^2(5z - 4)$ .

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