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Factor. $\newline$ $3y^2 + 8y + 4$

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Factor quadratics with other leading coefficients

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Q. Factor.

\newline

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: $y + 2$ $3y + 2$

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