Pregunta
Factor out the GCF: \( 15x^{3} - 25x^{2} + 10x \)
Ask by Salinas Craig. in South Africa
Jan 25,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The factored form is \(5x(x-1)(3x-2)\).
Solución
Factor the expression \( 15x^{3} - 25x^{2} + 10x \).
Factor the expression by following steps:
- step0: Factor:
\(15x^{3}-25x^{2}+10x\)
- step1: Factor the expression:
\(5\left(3x^{3}-5x^{2}+2x\right)\)
- step2: Factor the expression:
\(5x\left(3x^{2}-5x+2\right)\)
- step3: Factor the expression:
\(5x\left(x-1\right)\left(3x-2\right)\)
The factored form of the expression \(15x^{3} - 25x^{2} + 10x\) is \(5x(x-1)(3x-2)\).
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Simplifique esta solución Bonus Knowledge
To factor out the greatest common factor (GCF) from the expression \( 15x^{3} - 25x^{2} + 10x \), we first identify the GCF of the coefficients and the variable part. The coefficients are 15, -25, and 10, and the GCF of these numbers is 5. Since each term contains at least one \( x \), the common variable factor is \( x \). Thus, the overall GCF is \( 5x \). Now, we factor \( 5x \) out of each term: \[ 15x^{3} ÷ 5x = 3x^{2} \] \[ -25x^{2} ÷ 5x = -5x \] \[ 10x ÷ 5x = 2 \] Putting this together, we get: \[ 5x(3x^{2} - 5x + 2) \] So, the final factored expression is: \[ 5x(3x^{2} - 5x + 2) \]
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