Factor. 3y^2 + 8y + 4 ____

Identify Variables: Identify a, b, and c in the quadratic expression 3y^2 + 8y + 4 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 8 c = 4Find Two Numbers: Find two numbers that multiply to a*c (which is 3*4=12) and add up to b (which is 8). The two numbers that satisfy these conditions are 2 and 6 because: 2 * 6 = 12 2 + 6 = 8Rewrite Middle Term: Rewrite the middle term (8y) using the two numbers found in the previous step (2 and 6). 3y^2 + 8y + 4 can be rewritten as: 3y^2 + 2y + 6y + 4Factor by Grouping: Group the terms into two pairs and factor by grouping. Group (3y^2 + 2y) and (6y + 4). Factor out the greatest common factor from each group. From (3y^2 + 2y), factor out y: y(3y + 2) From (6y + 4), factor out 2: 2(3y + 2)Final Factored Form: Notice that both groups now have a common factor of (3y + 2). Factor out the common factor to get the final factored form: (y + 2)(3y + 2)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3y^2 + 8y + 4

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $3y^2 + 8y + 4$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 8$ $\newline$ $c = 4$
Find Two Numbers: Find two numbers that multiply to $a*c$ (which is $3*4=12$ ) and add up to $b$ (which is $8$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $6$ because: $\newline$ $2 \times 6 = 12$ $\newline$ $2 + 6 = 8$
Rewrite Middle Term: Rewrite the middle term $8y$ using the two numbers found in the previous step $2$ and $6$ . $3y^2 + 8y + 4$ can be rewritten as: $3y^2 + 2y + 6y + 4$
Factor by Grouping: Group the terms into two pairs and factor by grouping. $\newline$ Group $(3y^2 + 2y)$ and $(6y + 4)$ . $\newline$ Factor out the greatest common factor from each group. $\newline$ From $(3y^2 + 2y)$ , factor out $y$ : $\newline$ $y(3y + 2)$ $\newline$ From $(6y + 4)$ , factor out $2$ : $\newline$ $2(3y + 2)$
Final Factored Form: Notice that both groups now have a common factor of $3y + 2$ . Factor out the common factor to get the final factored form: $y + 2$ $3y + 2$