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

Identify Variables: Identify a, b, and c in the quadratic expression 3w^2 + 8w + 4 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 8 c = 4Find Multiplying 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 and 2+6 = 8.Rewrite Middle Term: Rewrite the middle term, 8w, using the two numbers found in the previous step. 3w^2 + 8w + 4 can be rewritten as 3w^2 + 2w + 6w + 4.Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms. (3w^2 + 2w) + (6w + 4)Factor Out Common Factors: Factor out the greatest common factor from each group. From the first group, factor out w: w(3w + 2) From the second group, factor out 2: 2(3w + 2)Final Factored Form: Notice that both groups contain the common factor (3w + 2). Factor this out. The factored form is (w + 2)(3w + 2).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3w^2 + 8w + 4

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $3w^2 + 8w + 4$ by comparing it with the standard form $ax^2 + bx + c$ .
$a = 3$
$b = 8$
$c = 4$
Find Multiplying 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 $2*6 = 12$ and $2+6 = 8$ .
Rewrite Middle Term: Rewrite the middle term, $8w$ , using the two numbers found in the previous step. $\newline$ $3w^2 + 8w + 4$ can be rewritten as $3w^2 + 2w + 6w + 4$ .
Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(3w^2 + 2w) + (6w + 4)$
Factor Out Common Factors: Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $w$ : $w(3w + 2)$ $\newline$ From the second group, factor out $2$ : $2(3w + 2)$
Final Factored Form: Notice that both groups contain the common factor $3w + 2$ . Factor this out. $\newline$ The factored form is $w + 2$ $3w + 2$ .