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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $8t^3 + 10t$

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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

8t^3 + 10t

Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms $8t^3$ and $10t$ . To do this, we will list the prime factors of the coefficients and include the common variables with the lowest exponents. $\newline$ $8t^3$ can be factored into $2 \times 2 \times 2 \times t \times t \times t$ . $\newline$ $10t$ can be factored into $2 \times 5 \times t$ . $\newline$ The common factors are $2$ and $t$ . $\newline$ The GCF is therefore $2t$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For $8t^3$ , we divide by $2t$ to get $4t^2$ . $\newline$ For $10t$ , we divide by $2t$ to get $5$ .
Write Original Polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors. $8t^3 + 10t = 2t(4t^2 + 5)$ .

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