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Factor by first factoring out the greatest common factor. \( 20 x^{3}+52 x^{2}-24 x \)

Ask by Ramos Burns. in the United States
Feb 17,2025

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Factor out the greatest common factor from \(20x^{3}+52x^{2}-24x\) to get \(4x(x+3)(5x-2)\).

Solución

Factor the expression \( 20x^3+52x^2-24x \). Factor the expression by following steps: - step0: Factor: \(20x^{3}+52x^{2}-24x\) - step1: Rewrite the expression: \(4x\times 5x^{2}+4x\times 13x-4x\times 6\) - step2: Factor the expression: \(4x\left(5x^{2}+13x-6\right)\) - step3: Factor the expression: \(4x\left(x+3\right)\left(5x-2\right)\) The expression \(20x^{3}+52x^{2}-24x\) can be factored by first factoring out the greatest common factor as \(4x(x+3)(5x-2)\).

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Mind Expander

To get started, let's find the greatest common factor (GCF) of the expression \( 20x^3 + 52x^2 - 24x \). The GCF here is \( 4x \) since 4 is the largest number that can evenly divide 20, 52, and 24, and \( x \) is the common variable in all terms. Now, factoring out \( 4x \) gives us: \[ 4x(5x^2 + 13x - 6) \] Next, we can focus on factoring the quadratic \( 5x^2 + 13x - 6 \). After looking for two numbers that multiply to \( 5 \times -6 = -30 \) and add up to \( 13 \), we can rewrite it using these numbers and then factor by grouping, arriving at: \[ 4x(5x - 1)(x + 6) \] Now the expression is fully factored as \( 4x(5x - 1)(x + 6) \)!

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