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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $4y^3 - 10y$

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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

4y^3 - 10y

Identify GCF: Identify the greatest common factor (GCF) of the terms $4y^3$ and $10y$ . The GCF is the largest factor that divides both terms. $\newline$ For $4y^3$ , the prime factors are $2 \times 2 \times y \times y \times y$ . $\newline$ For $10y$ , the prime factors are $2 \times 5 \times y$ . $\newline$ The common factors are $2$ and $y$ . $\newline$ The GCF of $4y^3$ and $10y$ is $10y$ $0$ .
Find Remaining Factors: Write each term as the product of the GCF and the remaining factors. $\newline$ For $4y^3$ , divide by the GCF $(2y)$ to find the remaining factor: $\frac{4y^3}{2y} = 2y^2$ . $\newline$ For $10y$ , divide by the GCF $(2y)$ to find the remaining factor: $\frac{10y}{2y} = 5$ .
Express as Product: Express the original polynomial as the product of the GCF and the sum of the remaining factors. $\newline$ $4y^3 - 10y = 2y(2y^2 - 5)$ .

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