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

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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

10c^2 + 4c

Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms $10c^2$ and $4c$ . To do this, we will list the factors of the coefficients and the powers of $c$ . $\newline$ Factors of $10$ : $1$ , $2$ , $5$ , $10$ $\newline$ Factors of $4$ : $1$ , $2$ , $4$ $\newline$ Common factors of the coefficients: $2$ $\newline$ Powers of $c$ in $10c^2$ : $4c$ $5$ $\newline$ Powers of $c$ in $4c$ : $c$ $\newline$ The common power of $c$ is the lowest power, which is $c$ . $\newline$ The GCF of $10c^2$ and $4c$ is therefore $c$ $3$ .
Divide by GCF: Now we will divide each term by the GCF to factor it out. $\newline$ For $10c^2$ , we have: $\newline$ $10c^2 \div 2c = 5c$ $\newline$ For $4c$ , we have: $\newline$ $4c \div 2c = 2$
Write as Product: We can now write the original polynomial as the product of the GCF and the factored terms: $10c^2 + 4c = 2c(5c + 2)$

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