Pregunta
Factor \( 3 x^{2}-11 x+6 \) \( (3 x-3)(x+2) \) \( (3 x+1)(x+1) \) \( (3 x-2)(x-3) \)
Ask by Warner Perkins. in the United States
Mar 17,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The factored form is \((x-3)(3x-2)\).
Solución
Factor the expression \( 3x^2-11x+6 \).
Factor the expression by following steps:
- step0: Factor:
\(3x^{2}-11x+6\)
- step1: Rewrite the expression:
\(3x^{2}+\left(-2-9\right)x+6\)
- step2: Calculate:
\(3x^{2}-2x-9x+6\)
- step3: Rewrite the expression:
\(x\times 3x-x\times 2-3\times 3x+3\times 2\)
- step4: Factor the expression:
\(x\left(3x-2\right)-3\left(3x-2\right)\)
- step5: Factor the expression:
\(\left(x-3\right)\left(3x-2\right)\)
The factored form of the expression \(3x^2-11x+6\) is \((x-3)(3x-2)\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To factor the quadratic expression \( 3x^2 - 11x + 6 \), we look for two numbers that multiply to \( 3 \times 6 = 18 \) and add to \(-11\). The pair that fits this criteria is \(-9\) and \(-2\). We can rewrite the middle term: \[ 3x^2 - 9x - 2x + 6 \] Now, factor by grouping: \[ 3x(x - 3) - 2(x - 3) \] Which factors to: \[ (3x - 2)(x - 3) \] Hence, the correct factorization is \( (3x - 2)(x - 3) \). As for the incorrect options provided: - \( (3x - 3)(x + 2) \) does not yield the correct middle term when expanded. - \( (3x + 1)(x + 1) \) also fails to match the original equation upon distribution.
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