Factor. z^2 + 6z + 5 ____

Identify Variables: Identify a, b, and c in the quadratic expression z^2 + 6z + 5. Compare z^2 + 6z + 5 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 6, and c = 5.Find Multiplying Numbers: Find two numbers that multiply to a*c (which is 1*5 = 5) and add up to b (which is 6). The numbers that satisfy these conditions are 1 and 5 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. z^2 + 6z + 5 can be written as z^2 + 1z + 5z + 5.Factor by Grouping: Factor by grouping. Group the terms to form pairs: (z^2 + 1z) + (5z + 5). Factor out the common factor from each pair: z(z + 1) + 5(z + 1).Factor out Common Binomial: Factor out the common binomial factor (z + 1). The factored form is (z + 1)(z + 5).

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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z^2 + 6z + 5

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $z^2 + 6z + 5$ . Compare $z^2 + 6z + 5$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 6$ , and $c = 5$ .
Find Multiplying Numbers: Find two numbers that multiply to $a*c$ (which is $1*5 = 5$ ) and add up to $b$ (which is $6$ ). $\newline$ The numbers that satisfy these conditions are $1$ and $5$ 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. $\newline$ $z^2 + 6z + 5$ can be written as $z^2 + 1z + 5z + 5$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to form pairs: $(z^2 + 1z) + (5z + 5)$ . $\newline$ Factor out the common factor from each pair: $z(z + 1) + 5(z + 1)$ .
Factor out Common Binomial: Factor out the common binomial factor $(z + 1)$ . $\newline$ The factored form is $(z + 1)(z + 5)$ .