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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $8t^3 + 10t^2$

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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

8t^3 + 10t^2

Find GCF of terms: We need to find the greatest common factor (GCF) of the terms $8t^3$ and $10t^2$ . To do this, we will list the factors of the coefficients and the powers of $t$ . $\newline$ Factors of $8$ : $1$ , $2$ , $4$ , $8$ $\newline$ Factors of $10$ : $1$ , $2$ , $10t^2$ $1$ , $10$ $\newline$ The common factors of the coefficients are $1$ and $2$ . $\newline$ Since both terms have at least $10t^2$ $5$ , we can factor out $10t^2$ $5$ as well. $\newline$ The GCF of $8t^3$ and $10t^2$ is therefore $10t^2$ $9$ .
Divide by GCF: Now we will divide each term by the GCF to find the remaining factors. $\newline$ For $8t^3$ , we have: $\newline$ $8t^3 \div 2t^2 = 4t$ $\newline$ For $10t^2$ , we have: $\newline$ $10t^2 \div 2t^2 = 5$
Write as product: We can now write the original polynomial as the product of the GCF and the remaining factors: $8t^3 + 10t^2 = 2t^2(4t + 5)$

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