Pregunta
Check Your Progress: Factor each \( t \) 1. \( x^{2}-9 x+14 \)
Ask by Norton Warner. in the United States
Jan 21,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( x^{2}-9x+14 = (x-7)(x-2) \)
Solución
Factor the expression \( x^{2}-9x+14 \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}-9x+14\)
- step1: Rewrite the expression:
\(x^{2}+\left(-2-7\right)x+14\)
- step2: Rewrite the expression:
\(x^{2}-2x-7x+14\)
- step3: Factor the expression:
\(x\left(x-2\right)-7\left(x-2\right)\)
- step4: Factor the expression:
\(\left(x-7\right)\left(x-2\right)\)
The factored form of the expression \(x^{2}-9x+14\) is \((x-7)(x-2)\).
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Simplifique esta solución Extra Insights
To factor the expression \( x^{2}-9x+14 \), look for two numbers that multiply to \( 14 \) (the constant term) and add up to \( -9 \) (the coefficient of \( x \)). The numbers \( -7 \) and \( -2 \) fit this requirement. Therefore, you can factor the quadratic as \( (x-7)(x-2) \). To check your work, you can expand \( (x-7)(x-2) \) to see if it equals the original expression: \( (x-7)(x-2) = x^2 - 2x - 7x + 14 = x^2 - 9x + 14 \). Ta-da! You've successfully factored the quadratic!
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