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

Identify Variables: Identify a, b, and c in the quadratic expression 3s^2 + 8s + 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 8s using the two numbers found in the previous step. 3s^2 + 8s + 4 can be rewritten as 3s^2 + 2s + 6s + 4.Factor by Grouping: Group the terms into two pairs and factor by grouping. (3s^2 + 2s) + (6s + 4) Now factor out the common factors from each pair. The common factor in the first pair is s, and in the second pair is 2. s(3s + 2) + 2(3s + 2)Factor Common Factor: Notice that (3s + 2) is a common factor in both terms. Factor out (3s + 2) from the expression. (3s + 2)(s + 2) is the factored form of the quadratic expression.

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3s^2 + 8s + 4

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $3s^2 + 8s + 4$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 8$ $\newline$ $c = 4$
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 $8s$ using the two numbers found in the previous step. $\newline$ $3s^2 + 8s + 4$ can be rewritten as $3s^2 + 2s + 6s + 4$ .
Factor by Grouping: Group the terms into two pairs and factor by grouping. $\newline$ $(3s^2 + 2s) + (6s + 4)$ $\newline$ Now factor out the common factors from each pair. $\newline$ The common factor in the first pair is $s$ , and in the second pair is $2$ . $\newline$ $s(3s + 2) + 2(3s + 2)$
Factor Common Factor: Notice that $(3s + 2)$ is a common factor in both terms. $\newline$ Factor out $(3s + 2)$ from the expression. $\newline$ $(3s + 2)(s + 2)$ is the factored form of the quadratic expression.