Pregunta
Factor the given trinomial. If the trinomial cannot be factored, indicate "Not Factorable". \[ x^{2}+5 x-14 \]
Ask by Carlson Garrett. in the United States
Feb 19,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( x^{2}+5x-14 = (x-2)(x+7) \)
Solución
Factor the expression \( x^{2}+5x-14 \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}+5x-14\)
- step1: Rewrite the expression:
\(x^{2}+\left(7-2\right)x-14\)
- step2: Calculate:
\(x^{2}+7x-2x-14\)
- step3: Rewrite the expression:
\(x\times x+x\times 7-2x-2\times 7\)
- step4: Factor the expression:
\(x\left(x+7\right)-2\left(x+7\right)\)
- step5: Factor the expression:
\(\left(x-2\right)\left(x+7\right)\)
The given trinomial \(x^{2}+5x-14\) can be factored as \((x-2)(x+7)\).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Bonus Knowledge
To factor the trinomial \( x^{2}+5x-14 \), we look for two numbers that multiply to \(-14\) (the constant term) and add up to \(5\) (the coefficient of the linear term). The numbers \(7\) and \(-2\) fit this perfectly because \(7 \times -2 = -14\) and \(7 + (-2) = 5\). Thus, we can write the factorization as: \[ (x + 7)(x - 2) \] So, the factors of the trinomial \( x^{2}+5x-14 \) are \( (x + 7)(x - 2) \).
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