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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $10z^3 + 4z^2$

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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 + 4z^2

Find GCF Factors: We need to find the greatest common factor (GCF) of the terms $10z^3$ and $4z^2$ . To do this, we will first list the factors of the coefficients ( $10$ and $4$ ) and the variables ( $z^3$ and $z^2$ ). $\newline$ Factors of $10$ : $1$ , $2$ , $5$ , $10$ $\newline$ Factors of $4$ : $1$ , $2$ , $4$ $\newline$ The common factors of the coefficients are $1$ and $2$ . $\newline$ Since $z^2$ is the lower power of $4z^2$ $8$ , it is the common factor in terms of the variable. $\newline$ The GCF of $10z^3$ and $4z^2$ is therefore $10$ $1$ .
Express Terms as Product: Now we will express each term as a product of the GCF and the remaining factors. $\newline$ For $10z^3$ , we divide it by the GCF $(2z^2)$ to find the remaining factor: $\newline$ $10z^3 \div 2z^2 = 5z$ $\newline$ So, $10z^3$ can be written as $2z^2 \times 5z$ .
Divide and Find Remaining Factor: For $4z^2$ , we divide it by the GCF $(2z^2)$ to find the remaining factor: $\newline$ $4z^2 \div 2z^2 = 2$ $\newline$ So, $4z^2$ can be written as $2z^2 \times 2$ .
Write Factored Form: We can now write the factored form of the polynomial $10z^3 + 4z^2$ using the GCF: $\newline$ $10z^3 + 4z^2$ $\newline$ $= 2z^2 * 5z + 2z^2 * 2$ $\newline$ $= 2z^2(5z + 2)$ $\newline$ This is the polynomial factored out by the greatest common factor.

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