Factor. d^2 + 12d + 11 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression d^2 + 12d + 11. Compare d^2 + 12d + 11 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 12, and c = 11.Find Multiplying Numbers: Find two numbers that multiply to a*c (which is 1*11=11) and add up to b (which is 12). We need to find two numbers m and n such that: m * n = 11 m + n = 12 The numbers that satisfy these conditions are 1 and 11 because: 1 * 11 = 11 1 + 11 = 12Rewrite Quadratic Expression: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. d^2 + 12d + 11 can be rewritten as: d^2 + d + 11d + 11Factor by Grouping: Factor by grouping. Group the terms to factor out the common factors: (d^2 + d) + (11d + 11) Factor out a d from the first group and 11 from the second group: d(d + 1) + 11(d + 1)Factor out Common Binomial: Factor out the common binomial factor. Both groups contain the common factor (d + 1), so factor this out: (d + 1)(d + 11)

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Factor. $\newline$ $d^2 + 12d + 11$

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

d^2 + 12d + 11

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $d^2 + 12d + 11$ . Compare $d^2 + 12d + 11$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find Multiplying Numbers: Find two numbers that multiply to $a*c$ (which is $1*11=11$ ) and add up to $b$ (which is $12$ ). $\newline$ We need to find two numbers $m$ and $n$ such that: $\newline$ $m * n = 11$ $\newline$ $m + n = 12$ $\newline$ The numbers that satisfy these conditions are $1$ and $11$ because: $\newline$ $1*11=11$ $0$ $\newline$ $1*11=11$ $1$
Rewrite Quadratic Expression: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ $d^2 + 12d + 11$ can be rewritten as: $\newline$ $d^2 + d + 11d + 11$
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to factor out the common factors: $\newline$ $(d^2 + d) + (11d + 11)$ $\newline$ Factor out a $d$ from the first group and $11$ from the second group: $\newline$ $d(d + 1) + 11(d + 1)$
Factor out Common Binomial: Factor out the common binomial factor. $\newline$ Both groups contain the common factor $(d + 1)$ , so factor this out: $\newline$ $(d + 1)(d + 11)$