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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $8z^3 - 6z^2$

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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

8z^3 - 6z^2

Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms $8z^3$ and $6z^2$ . To do this, we will first list the prime factors of the coefficients and the common variables. $\newline$ $8z^3 = 2 \times 2 \times 2 \times z \times z \times z$ $\newline$ $6z^2 = 2 \times 3 \times z \times z$ $\newline$ The common factors are $2$ , $z$ , and $z$ . $\newline$ $2 \times z \times z = 2z^2$ $\newline$ So, the GCF of $8z^3$ and $6z^2$ is $6z^2$ $0$ .
Express Terms with GCF: Now we will express each term as the product of the GCF and the remaining factors. $\newline$ For $8z^3$ , we have: $\newline$ $8z^3 = 2 \times 2 \times 2 \times z \times z \times z$ $\newline$ $8z^3 = 2z^2 \times 4z$ $\newline$ For $6z^2$ , we have: $\newline$ $6z^2 = 2 \times 3 \times z \times z$ $\newline$ $6z^2 = 2z^2 \times 3$
Factor Out GCF: We can now factor out the GCF from the polynomial $8z^3 - 6z^2$ .
$8z^3 - 6z^2$
$= 2z^2 * 4z - 2z^2 * 3$
$= 2z^2(4z - 3)$
This is the factored form of the polynomial with the GCF factored out.

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