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

Identify a, b, c: Identify a, b, and c in the quadratic expression 3t^2 + 8t + 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 (3*4 = 12) and add up to b (8). We need to find two numbers that multiply to 12 and add up to 8. The numbers 2 and 6 satisfy these conditions because 2*6 = 12 and 2+6 = 8.Rewrite middle term: Rewrite the middle term 8t using the two numbers found in the previous step. The expression 3t^2 + 8t + 4 can be rewritten as 3t^2 + 2t + 6t + 4 by splitting the middle term.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (3t^2 + 2t) + (6t + 4) Now factor out the common factors from each group. From the first group, we can factor out t: t(3t + 2) From the second group, we can factor out 2: 2(3t + 2)Notice common factor: Notice that both groups contain the common factor (3t + 2). We can factor out (3t + 2) from the entire expression. The factored form is (t + 2)(3t + 2).

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

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

\newline

3t^2 + 8t + 4

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3t^2 + 8t + 4$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 8$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ ( $3*4 = 12$ ) and add up to $b$ ( $8$ ). $\newline$ We need to find two numbers that multiply to $12$ and add up to $8$ . $\newline$ The numbers $2$ and $6$ satisfy these conditions because $2*6 = 12$ and $2+6 = 8$ .
Rewrite middle term: Rewrite the middle term $8t$ using the two numbers found in the previous step. $\newline$ The expression $3t^2 + 8t + 4$ can be rewritten as $3t^2 + 2t + 6t + 4$ by splitting the middle term.
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(3t^2 + 2t) + (6t + 4)$ $\newline$ Now factor out the common factors from each group. $\newline$ From the first group, we can factor out $t$ : $t(3t + 2)$ $\newline$ From the second group, we can factor out $2$ : $2(3t + 2)$
Notice common factor: Notice that both groups contain the common factor $3t + 2$ . We can factor out $3t + 2$ from the entire expression. The factored form is $t + 2$ $(3t + 2)$ .