Question
Factor the given polynomial \[ x^{2}-9 x+20 \] Select the correct choice below and, if necessary, fill in the answer box within yo A. \( x^{2}-9 x+20=\square \) - B. The polynomial is prime.
Ask by Garrett Harris. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The polynomial \( x^{2} - 9x + 20 \) factors to \( (x - 4)(x - 5) \).
Solution
To factor the polynomial \( x^{2} - 9x + 20 \), we look for two numbers that multiply to **20** and add up to **-9**.
1. **Identify the factors of 20:**
- \(1 \times 20\)
- \(2 \times 10\)
- \(4 \times 5\)
2. **Determine which pair adds up to -9:**
- \(4 + 5 = 9\)
- \(-4 + (-5) = -9\)
The pair \(-4\) and \(-5\) satisfies both conditions.
3. **Write the factored form:**
\[
x^{2} - 9x + 20 = (x - 4)(x - 5)
\]
**Correct Choice:**
**A.**
\[
x^{2} - 9x + 20 = (x - 4)(x - 5)
\]
Choice **B** is incorrect because the polynomial is not prime; it can be factored as shown above.
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
To factor the polynomial \( x^{2}-9 x+20 \), we look for two numbers that multiply to 20 (the constant term) and add up to -9 (the coefficient of the x term). The numbers -4 and -5 fit the bill since \(-4 \times -5 = 20\) and \(-4 + -5 = -9\). Thus, we can rewrite the polynomial as: \[ x^{2}-9 x+20 = (x-4)(x-5) \] So, the correct choice is: A. \( x^{2}-9 x+20=(x-4)(x-5) \)
