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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $4u^2 + 8u$

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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

4u^2 + 8u

Find GCF Factors: We need to find the greatest common factor (GCF) of the terms $4u^2$ and $8u$ . To do this, we will list the factors of the coefficients and the variables separately. $\newline$ Factors of $4$ : $1$ , $2$ , $4$ $\newline$ Factors of $8$ : $1$ , $2$ , $4$ , $8$ $\newline$ The common factors of the coefficients are $1$ , $2$ , and $4$ . $\newline$ For the variables, since both terms have ' $8u$ $4$ ', we take the lowest power of ' $8u$ $4$ ' present in both terms, which is $8u$ $6$ . $\newline$ The GCF of $4u^2$ and $8u$ is therefore $8u$ $9$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For $4u^2$ , we divide by $4u$ to get $u$ . $\newline$ $4u^2 \div 4u = u$ $\newline$ For $8u$ , we divide by $4u$ to get $2$ . $\newline$ $8u \div 4u = 2$
Write Factored Form: We can now write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $4u^2 + 8u = 4u(u + 2)$ $\newline$ This is the factored form of the polynomial.

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