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

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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

2t^3 - 8t

Find GCF Factors: We need to find the greatest common factor (GCF) of the terms $2t^3$ and $-8t$ . To do this, we will list the factors of the coefficients and the powers of $t$ . $\newline$ Factors of $2$ : $1$ , $2$ $\newline$ Factors of $8$ : $1$ , $2$ , $4$ , $8$ $\newline$ Powers of $t$ in $2t^3$ : $t$ , $-8t$ $4$ , $-8t$ $5$ $\newline$ Powers of $t$ in $-8t$ : $t$ $\newline$ The common factors of the coefficients are $2$ , and the lowest power of $t$ that is common to both terms is $t$ . $\newline$ So, the GCF is $t$ $2$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For $2t^3$ , we divide by $2t$ to get $t^2$ . $\newline$ For $-8t$ , we divide by $2t$ to get $-4$ .
Write Original Polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors. $\newline$ $2t^3 - 8t = 2t(t^2 - 4)$

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