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Factor. $\newline$ $y^2 + 6y + 5$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

y^2 + 6y + 5

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $y^2 + 6y + 5$ . Compare $y^2 + 6y + 5$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find Numbers for $a*c$ : Find two numbers that multiply to $a*c$ (which is $1*5 = 5$ ) and add up to $b$ (which is $6$ ). $\newline$ The two numbers that satisfy these conditions are $1$ and $5$ because: $\newline$ $1 * 5 = 5$ and $1 + 5 = 6$ .
Rewrite Quadratic Expression: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ $y^2 + 6y + 5$ can be rewritten as $y^2 + 1y + 5y + 5$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to find common factors: $\newline$ $(y^2 + 1y) + (5y + 5)$ $\newline$ Factor out a $y$ from the first group and a $5$ from the second group: $\newline$ $y(y + 1) + 5(y + 1)$ .
Factor out Common Binomial: Factor out the common binomial factor $(y + 1)$ . The factored form is $(y + 1)(y + 5)$ .

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