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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $4c^3 + 6c^2$

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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

4c^3 + 6c^2

Identify GCF: Identify the greatest common factor (GCF) of the terms $4c^3$ and $6c^2$ . The GCF is the highest number that divides both coefficients ( $4$ and $6$ ) and the highest power of $c$ that is in both terms ( $c^2$ ). $\newline$ The GCF of the coefficients $4$ and $6$ is $2$ . Both terms have at least $c^2$ in them. $\newline$ So, the GCF of $4c^3$ and $6c^2$ is $6c^2$ $2$ .
Divide by GCF: Divide each term by the GCF to find the remaining factors. $\newline$ For $4c^3$ , divide by $2c^2$ to get $2c$ . $\newline$ For $6c^2$ , divide by $2c^2$ to get $3$ .
Write as Product: Write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $4c^3 + 6c^2 = 2c^2(2c) + 2c^2(3) = 2c^2(2c + 3)$ .

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