Factor. 3y^3 + 2y^2 + 15y + 10 ______

Group Terms: Look for common factors in pairs of terms. We will group the terms into two pairs and look for common factors in each pair. Group 1: 3y^3 + 2y^2 Group 2: 15y + 10Factor First Group: Factor out the greatest common factor from the first group. The greatest common factor of 3y^3 and 2y^2 is y^2. So, 3y^3 + 2y^2 = y^2(3y + 2)Factor Second Group: Factor out the greatest common factor from the second group. The greatest common factor of 15y and 10 is 5. So, 15y + 10 = 5(3y + 2)Write Factored Groups: Write the expression with the factored groups. Now we have: y^2(3y + 2) + 5(3y + 2)Factor Common Binomial: Factor out the common binomial factor. Both terms have a common factor of (3y + 2). So, y^2(3y + 2) + 5(3y + 2) = (y^2 + 5)(3y + 2)

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Q. Factor.

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3y^3 + 2y^2 + 15y + 10

Group Terms: Look for common factors in pairs of terms. $\newline$ We will group the terms into two pairs and look for common factors in each pair. $\newline$ Group $1$ : $3y^3 + 2y^2$ $\newline$ Group $2$ : $15y + 10$
Factor First Group: Factor out the greatest common factor from the first group. $\newline$ The greatest common factor of $3y^3$ and $2y^2$ is $y^2$ . $\newline$ So, $3y^3 + 2y^2 = y^2(3y + 2)$
Factor Second Group: Factor out the greatest common factor from the second group. $\newline$ The greatest common factor of $15y$ and $10$ is $5$ . $\newline$ So, $15y + 10 = 5(3y + 2)$
Write Factored Groups: Write the expression with the factored groups. $\newline$ Now we have: $\newline$ $y^2(3y + 2) + 5(3y + 2)$
Factor Common Binomial: Factor out the common binomial factor. $\newline$ Both terms have a common factor of $(3y + 2)$ . $\newline$ So, $y^2(3y + 2) + 5(3y + 2) = (y^2 + 5)(3y + 2)$