Factor. k^2 + 6k + 5 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression k^2 + 6k + 5. Compare k^2 + 6k + 5 with the standard form ax^2 + bx + c. Here, a = 1, b = 6, and c = 5.Find product and sum: Find two numbers whose product is ac (since a = 1, just c) and whose sum is b. We need two numbers that multiply to 5 and add up to 6. The numbers 2 and 3 satisfy these conditions because 2 * 3 = 6 and 2 + 3 = 5.Rewrite quadratic expression: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. k^2 + 6k + 5 can be rewritten as k^2 + 2k + 3k + 5.Factor by grouping: Factor by grouping. Group the terms to factor by common factors: (k^2 + 2k) + (3k + 5) Factor out the common factor from each group: k(k + 2) + 3(k + 2)Factor out common binomial: Factor out the common binomial factor. Since both terms contain the factor (k + 2), factor this out: (k + 2)(k + 3)

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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k^2 + 6k + 5

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $k^2 + 6k + 5$ . Compare $k^2 + 6k + 5$ with the standard form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find product and sum: Find two numbers whose product is $ac$ (since $a = 1$ , just $c$ ) and whose sum is $b$ . We need two numbers that multiply to $5$ and add up to $6$ . The numbers $2$ and $3$ satisfy these conditions because $2 \times 3 = 6$ and $2 + 3 = 5$ .
Rewrite quadratic expression: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ $k^2 + 6k + 5$ can be rewritten as $k^2 + 2k + 3k + 5$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms to factor by common factors: $\newline$ $(k^2 + 2k) + (3k + 5)$ $\newline$ Factor out the common factor from each group: $\newline$ $k(k + 2) + 3(k + 2)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ Since both terms contain the factor $(k + 2)$ , factor this out: $\newline$ $(k + 2)(k + 3)$