Question
The trinomial \( x^{2}+7 x-18 \) factors into (Factor completely.)
Ask by Ruiz Hodges. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The trinomial factors to \( (x + 9)(x - 2) \).
Solution
1. We need two numbers that multiply to \( -18 \) (the constant term) and add to \( 7 \) (the coefficient of \( x \)).
2. Consider the pair \( 9 \) and \( -2 \), because:
- \( 9 \times (-2) = -18 \)
- \( 9 + (-2) = 7 \)
3. Therefore, the trinomial factors as:
\[
x^2 + 7x - 18 = (x + 9)(x - 2)
\]
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Simplify this solution Beyond the Answer
To factor the trinomial \( x^{2}+7x-18 \), we look for two numbers that multiply to \(-18\) (the constant term) and add up to \(7\) (the coefficient of \(x\)). Those two numbers are \(9\) and \(-2\), since \(9 \times -2 = -18\) and \(9 + (-2) = 7\). Thus, we can write the factored form as \( (x + 9)(x - 2) \). So, the complete factorization of \( x^{2}+7x-18 \) is \( (x + 9)(x - 2) \).
