Factor. 3d^2 + 10d + 7 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 3d^2 + 10d + 7 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 10 c = 7Find Factors and Sum: Find two numbers that multiply to a*c (which is 3*7=21) and add up to b (which is 10). We need to find two numbers that satisfy these conditions. After checking possible pairs of factors of 21, we find that 3 and 7 are the numbers we are looking for because: 3 * 7 = 21 3 + 7 = 10Rewrite Middle Term: Rewrite the middle term (10d) using the two numbers found in the previous step (3 and 7) to split it into two terms. 3d^2 + 10d + 7 can be rewritten as: 3d^2 + 3d + 7d + 7Factor 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 + 3d, we can factor out 3d: 3d(d + 1) From 7d + 7, we can factor out 7: 7(d + 1) Now we have: 3d(d + 1) + 7(d + 1)Factor out Common Factor: Factor out the common binomial factor (d + 1) from both terms. The factored form of the expression is: (3d + 7)(d + 1)

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Factor. $\newline$ $3d^2 + 10d + 7$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3d^2 + 10d + 7

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3d^2 + 10d + 7$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 10$ $\newline$ $b$ $0$
Find Factors and Sum: Find two numbers that multiply to $a*c$ (which is $3*7=21$ ) and add up to $b$ (which is $10$ ). $\newline$ We need to find two numbers that satisfy these conditions. $\newline$ After checking possible pairs of factors of $21$ , we find that $3$ and $7$ are the numbers we are looking for because: $\newline$ $3 \times 7 = 21$ $\newline$ $3 + 7 = 10$
Rewrite Middle Term: Rewrite the middle term ( $10d$ ) using the two numbers found in the previous step ( $3$ and $7$ ) to split it into two terms. $\newline$ $3d^2 + 10d + 7$ can be rewritten as: $\newline$ $3d^2 + 3d + 7d + 7$
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 $3d^2 + 3d$ , we can factor out $3d$ : $\newline$ $3d(d + 1)$ $\newline$ From $7d + 7$ , we can factor out $7$ : $\newline$ $7(d + 1)$ $\newline$ Now we have: $\newline$ $3d(d + 1) + 7(d + 1)$
Factor out Common Factor: Factor out the common binomial factor $(d + 1)$ from both terms. $\newline$ The factored form of the expression is: $\newline$ $(3d + 7)(d + 1)$