Factor. n^2 + 6n + 5 ____

Identify Variables: Identify a, b, and c in the quadratic expression n^2 + 6n + 5. Compare n^2 + 6n + 5 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 6, and c = 5.Find Product and Sum: Find two numbers whose product is equal to ac (since a = 1, just c) and whose sum is equal to b. We need two numbers that multiply to 5 and add up to 6. The numbers 1 and 5 fit this requirement because: 1 * 5 = 5 and 1 + 5 = 6.Split Middle Term: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. n^2 + 6n + 5 can be written as n^2 + 1n + 5n + 5.Factor by Grouping: Factor by grouping. Group the terms to factor by common terms: (n^2 + 1n) + (5n + 5) Factor out an n from the first group and a 5 from the second group: n(n + 1) + 5(n + 1).Factor Common Binomial: Factor out the common binomial factor. Both groups contain the common factor (n + 1), so factor this out: (n + 1)(n + 5).

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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n^2 + 6n + 5

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $n^2 + 6n + 5$ . Compare $n^2 + 6n + 5$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 6$ , and $c = 5$ .
Find Product and Sum: Find two numbers whose product is equal to $ac$ (since $a = 1$ , just $c$ ) and whose sum is equal to $b$ . We need two numbers that multiply to $5$ and add up to $6$ . The numbers $1$ and $5$ fit this requirement because: $1 \times 5 = 5$ and $1 + 5 = 6$ .
Split Middle Term: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $n^2 + 6n + 5$ can be written as $n^2 + 1n + 5n + 5$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to factor by common terms: $\newline$ $(n^2 + 1n) + (5n + 5)$ $\newline$ Factor out an $n$ from the first group and a $5$ from the second group: $\newline$ $n(n + 1) + 5(n + 1)$ .
Factor Common Binomial: Factor out the common binomial factor. $\newline$ Both groups contain the common factor $(n + 1)$ , so factor this out: $\newline$ $(n + 1)(n + 5)$ .