Question
Factor the irinomial. \( r^{2}+12 r+32 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( r^{2}+12 r+32=\square \) (Factor completely.) B. The polynomial is prime.
Ask by Summers Marshall. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( r^{2}+12 r+32=(r+4)(r+8) \)
Solution
To factor the trinomial \( r^{2} + 12r + 32 \), we look for two numbers that add up to 12 and multiply to 32.
1. **Identify the pair of numbers:**
- \(4 + 8 = 12\)
- \(4 \times 8 = 32\)
2. **Write the factored form:**
\[
r^{2} + 12r + 32 = (r + 4)(r + 8)
\]
**Answer:**
**A.** \( r^{2}+12 r+32=(r+4)(r+8) \) (Factor completely.)
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Simplify this solution The Deep Dive
To factor the trinomial \( r^{2}+12 r+32 \), we need to find two numbers that multiply to 32 and add to 12. Those numbers are 4 and 8. Thus, we can rewrite the trinomial as: \( r^{2}+12 r+32 = (r + 4)(r + 8) \). So, the correct choice is A: \( r^{2}+12 r+32=(r + 4)(r + 8) \).
