Question

factoriza completamente la expresión.
$4x^4 - 4x^3 - 8x^2$
muestra tu trabajo aquí
pista: para añadir un exponente ($x^y$), escribe
\exponente\ o presiona \^\
escribe tu respuesta
revisar

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(4x^4\), \(-4x^3\), and \(-8x^2\). The GCF of the coefficients \(4\), \(-4\), and \(-8\) is \(4\), and the GCF of the variable parts \(x^4\), \(x^3\), and \(x^2\) is \(x^2\). So, factor out \(4x^2\):
\(4x^4 - 4x^3 - 8x^2 = 4x^2(x^2 - x - 2)\)

Step2: Factor the quadratic

Now, factor the quadratic \(x^2 - x - 2\). We need two numbers that multiply to \(-2\) and add to \(-1\). Those numbers are \(-2\) and \(1\). So, we can write:
\(x^2 - x - 2 = (x - 2)(x + 1)\)

Step3: Combine the factors

Putting it all together, the completely factored form of the original expression is:
\(4x^2(x - 2)(x + 1)\)

Answer:

\(4x^2(x - 2)(x + 1)\)