Pregunta
Question 15 Factor the trinomial \( x^{2}-7 x+10 \) \( \square \) Next Question
Ask by Barber Santiago. in the United States
Jan 25,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( x^{2}-7x+10 = (x-5)(x-2) \)
Solución
Factor the expression \( x^{2}-7x+10 \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}-7x+10\)
- step1: Rewrite the expression:
\(x^{2}+\left(-2-5\right)x+10\)
- step2: Rewrite the expression:
\(x^{2}-2x-5x+10\)
- step3: Factor the expression:
\(x\left(x-2\right)-5\left(x-2\right)\)
- step4: Factor the expression:
\(\left(x-5\right)\left(x-2\right)\)
The trinomial \(x^{2}-7x+10\) can be factored as \((x-5)(x-2)\).
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Extra Insights
The trinomial \( x^{2}-7x+10 \) factors into the expression \( (x-2)(x-5) \). You can find the factors by looking for two numbers that multiply to 10 (the constant term) and add up to -7 (the coefficient of the linear term). In this case, -2 and -5 do just the trick! Once you have factored it, you can quickly check your work by expanding: \( (x-2)(x-5) \) gives you \( x^{2} - 7x + 10 \) again. It's like a fun mathematical magic trick!
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