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Factor. $\newline$ $n^2 + 24n + 23$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

n^2 + 24n + 23

Identify Coefficients: Identify the coefficients for $n^2$ , $n$ , and the constant term in the quadratic expression $n^2 + 24n + 23$ . The coefficient of $n^2$ is $1$ ( $a = 1$ ), the coefficient of $n$ is $24$ ( $b = 24$ ), and the constant term is $23$ ( $n$ $0$ ).
Find Multiplying Numbers: Find two numbers that multiply to give the constant term, $c = 23$ , and add up to the coefficient of the $n$ term, $b = 24$ . The numbers that satisfy these conditions are $1$ and $23$ because $1 \times 23 = 23$ and $1 + 23 = 24$ .
Write Factored Form: Write the factored form of the quadratic expression using the two numbers found in the previous step. $\newline$ The factored form is $(n + 1)(n + 23)$ .

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