Pregunta
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\(4(x-1)(x+9)\)
Solución
Factor the expression \( 4x^2+32x-36 \).
Factor the expression by following steps:
- step0: Factor:
\(4x^{2}+32x-36\)
- step1: Rewrite the expression:
\(4x^{2}+4\times 8x-4\times 9\)
- step2: Factor the expression:
\(4\left(x^{2}+8x-9\right)\)
- step3: Factor the expression:
\(4\left(x-1\right)\left(x+9\right)\)
The factored form of \(4x^{2}+32x-36\) is \(4(x-1)(x+9)\).
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Simplifique esta solución Bonus Knowledge
To factor the expression \( 4x^{2} + 32x - 36 \), we can start by factoring out the greatest common factor (GCF) of the coefficients. The GCF here is 4: \( 4(x^{2} + 8x - 9) \) Next, we focus on the quadratic expression \( x^{2} + 8x - 9 \). We look for two numbers that multiply to -9 and add to 8. These numbers are 9 and -1. Therefore, we can factor the quadratic: \( 4(x + 9)(x - 1) \) So, the completely factored form of \( 4x^{2} + 32x - 36 \) is \( 4(x + 9)(x - 1) \).
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