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

Identify a, b, c: Identify a, b, and c in the quadratic expression 3n^2 + 10n + 7. Compare 3n^2 + 10n + 7 with the standard form ax^2 + bx + c. a = 3 b = 10 c = 7Find Numbers Multiply Add: 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 that multiply to 21 (such as 1 and 21, 3 and 7), we find that: 1 * 21 = 21 1 + 21 = 22 This pair does not work since their sum is not 10. 3 * 7 = 21 3 + 7 = 10 This pair works since their sum is 10. Two numbers: 3, 7Rewrite Middle Term: Rewrite the middle term 10n using the two numbers found in Step 2. 10n can be written as the sum of 3n and 7n. So, 3n^2 + 10n + 7 can be rewritten as 3n^2 + 3n + 7n + 7.Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms: (3n^2 + 3n) + (7n + 7) Factor out the greatest common factor from each group: 3n(n + 1) + 7(n + 1)Factor out Common Binomial: Factor out the common binomial factor (n + 1). We now have 3n(n + 1) + 7(n + 1), which can be factored as: (3n + 7)(n + 1)

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

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3n^2 + 10n + 7

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3n^2 + 10n + 7$ . Compare $3n^2 + 10n + 7$ with the standard form $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find Numbers Multiply Add: 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 that multiply to $21$ (such as $1$ and $21$ , $3$ and $7$ ), we find that: $\newline$ $1 \times 21 = 21$ $\newline$ $3*7=21$ $0$ $\newline$ This pair does not work since their sum is not $10$ . $\newline$ $3*7=21$ $2$ $\newline$ $3*7=21$ $3$ $\newline$ This pair works since their sum is $10$ . $\newline$ Two numbers: $3$ , $7$
Rewrite Middle Term: Rewrite the middle term $10n$ using the two numbers found in Step $2$ . $\newline$ $10n$ can be written as the sum of $3n$ and $7n$ . $\newline$ So, $3n^2 + 10n + 7$ can be rewritten as $3n^2 + 3n + 7n + 7$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms: $\newline$ $(3n^2 + 3n) + (7n + 7)$ $\newline$ Factor out the greatest common factor from each group: $\newline$ $3n(n + 1) + 7(n + 1)$
Factor out Common Binomial: Factor out the common binomial factor $(n + 1)$ . We now have $3n(n + 1) + 7(n + 1)$ , which can be factored as: $(3n + 7)(n + 1)$