Question
Factor each completely \[ \times \quad n^{2}+13 n+40 \]
Ask by Rogers George. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
n^2 + 13n + 40 = (n + 5)(n + 8)
\]
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Beyond the Answer
To factor the quadratic expression \( n^{2} + 13n + 40 \), we look for two numbers that multiply to 40 (the constant term) and add up to 13 (the coefficient of the linear term). The numbers 8 and 5 fit the bill, as \( 8 \times 5 = 40 \) and \( 8 + 5 = 13 \). So, we can write the expression as: \[ (n + 8)(n + 5) \] This means the factored form of \( n^{2} + 13n + 40 \) is \( (n + 8)(n + 5) \). And there you have it, a perfectly factored quadratic ready for action!