Pregunta
Factor the trinomial completely. \[ x^{2}-23 x+60 \]
Ask by Gough Estrada. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( x^{2}-23x+60 = (x-20)(x-3) \)
Solución
Factor the expression \( x^{2}-23x+60 \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}-23x+60\)
- step1: Rewrite the expression:
\(x^{2}+\left(-3-20\right)x+60\)
- step2: Rewrite the expression:
\(x^{2}-3x-20x+60\)
- step3: Factor the expression:
\(x\left(x-3\right)-20\left(x-3\right)\)
- step4: Factor the expression:
\(\left(x-20\right)\left(x-3\right)\)
The trinomial \(x^{2}-23x+60\) can be factored completely as \((x-20)(x-3)\).
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Extra Insights
To factor the trinomial \( x^{2}-23x+60 \), we need to find two numbers that multiply to 60 (the constant term) and add up to -23 (the coefficient of the middle term). These two numbers are -20 and -3 because: - (-20) + (-3) = -23 - (-20) * (-3) = 60 Thus, we can express the trinomial as: \[ (x - 20)(x - 3) \] So the factored form of the trinomial \( x^{2}-23x+60 \) is \( (x - 20)(x - 3) \).
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