Question
Factor the given polynomial. \[ x^{2}+9 x+14 \] Select the correct choice below A. \( x^{2}+9 x+14= \) B. The polynomial is prime
Ask by Ross Mcfarlane. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The factored form of the polynomial is \( (x + 2)(x + 7) \).
Solution
To factor the quadratic polynomial \( x^{2} + 9x + 14 \), we look for two numbers that add up to 9 and multiply to 14.
1. **Identify the coefficients:**
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = 9 \) (coefficient of \( x \))
- \( c = 14 \) (constant term)
2. **Find two numbers that satisfy:**
- **Sum:** \( m + n = 9 \)
- **Product:** \( m \times n = 14 \)
3. **Determine the numbers:**
- The numbers 2 and 7 satisfy both conditions because:
- \( 2 + 7 = 9 \)
- \( 2 \times 7 = 14 \)
4. **Write the factored form:**
\[
x^{2} + 9x + 14 = (x + 2)(x + 7)
\]
**Correct Choice:**
**A.**
\[
x^{2} + 9x + 14 = (x + 2)(x + 7)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To factor the polynomial \( x^{2}+9x+14 \), we need to find two numbers that multiply to 14 (the constant term) and add up to 9 (the coefficient of the linear term). The numbers 7 and 2 fit these requirements perfectly! Therefore, we can write the factored form as \( (x+7)(x+2) \). So the answer is: A. \( x^{2}+9x+14=(x+7)(x+2) \)
