Factor. 3d^2 + 5d + 2 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 3d^2 + 5d + 2 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 5 c = 2Find two numbers: Find two numbers that multiply to a*c (which is 3*2=6) and add up to b (which is 5). The two numbers that satisfy these conditions are 2 and 3 because: 2 * 3 = 6 2 + 3 = 5Rewrite middle term: Rewrite the middle term (5d) using the two numbers found in the previous step (2 and 3) to split it into two terms. 3d^2 + 5d + 2 can be rewritten as: 3d^2 + 2d + 3d + 2Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together, then factor out the common factors from each group. From 3d^2 + 2d, factor out d: d(3d + 2) From 3d + 2, factor out 1: 1(3d + 2) Now we have: d(3d + 2) + 1(3d + 2)Factor out common binomial: Factor out the common binomial factor (3d + 2) from both groups. (3d + 2) is the common factor, so we get: (d + 1)(3d + 2)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3d^2 + 5d + 2

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3d^2 + 5d + 2$ by comparing it with the standard form $ax^2 + bx + c$ .
$a = 3$
$b = 5$
$b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $3*2=6$ ) and add up to $b$ (which is $5$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $3$ because: $\newline$ $2 * 3 = 6$ $\newline$ $2 + 3 = 5$
Rewrite middle term: Rewrite the middle term $5d$ using the two numbers found in the previous step $2$ and $3$ to split it into two terms. $\newline$ $3d^2 + 5d + 2$ can be rewritten as: $\newline$ $3d^2 + 2d + 3d + 2$
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together, then factor out the common factors from each group. $\newline$ From $3d^2 + 2d$ , factor out $d$ : $\newline$ $d(3d + 2)$ $\newline$ From $3d + 2$ , factor out $1$ : $\newline$ $1(3d + 2)$ $\newline$ Now we have: $\newline$ $d(3d + 2) + 1(3d + 2)$
Factor out common binomial: Factor out the common binomial factor $(3d + 2)$ from both groups. $(3d + 2)$ is the common factor, so we get: $(d + 1)(3d + 2)$