Question
\( v^{2}-7 v+10=\square \) (Type your answer in factored
Ask by Hill Howell. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( (v - 2)(v - 5) \)
Solution
The quadratic expression \( v^{2} - 7v + 10 \) can be factored by finding two numbers that multiply to \(10\) and add up to \(-7\).
1. **Identify the pairs of factors of 10:**
- \(1 \times 10\)
- \(2 \times 5\)
- \(-2 \times -5\)
2. **Determine which pair adds up to \(-7\):**
- \(-2 + (-5) = -7\)
3. **Write the factored form:**
\[
v^{2} - 7v + 10 = (v - 2)(v - 5)
\]
**Answer:**
\[(v - 2)(v - 5)\]
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Simplify this solution Beyond the Answer
To factor the quadratic equation \( v^{2} - 7v + 10 \), we need to find two numbers that multiply to \( 10 \) (the constant term) and add up to \( -7 \) (the coefficient of \( v \)). Those numbers are \( -5 \) and \( -2 \). Thus, we can express the factored form as: \[ (v - 5)(v - 2) = \square \]
