Question

question
factor completely.
\\(-34x^4y^4z^5 - x^2y^2z^4\\)

Explanation:

Step1: Identify the GCF of the terms

The terms are \(-34x^{4}y^{4}z^{5}\) and \(-x^{2}y^{2}z^{4}\). For the coefficients, the GCF of 34 and 1 is 1 (and we consider the negative sign). For \(x\): the lowest power is \(x^{2}\). For \(y\): the lowest power is \(y^{2}\). For \(z\): the lowest power is \(z^{4}\). So the GCF is \(-x^{2}y^{2}z^{4}\) (we can also use \( -x^{2}y^{2}z^{4}\) or \(x^{2}y^{2}z^{4}\), but let's use the negative one to make the first term positive when factored out).

Step2: Factor out the GCF

Factor out \(-x^{2}y^{2}z^{4}\) from \(-34x^{4}y^{4}z^{5}-x^{2}y^{2}z^{4}\).

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We can check by distributing back: \(-x^{2}y^{2}z^{4}\times34x^{2}y^{2}z=-34x^{4}y^{4}z^{5}\) and \(-x^{2}y^{2}z^{4}\times1=-x^{2}y^{2}z^{4}\), which matches the original expression.

Answer:

\(-x^{2}y^{2}z^{4}(34x^{2}y^{2}z + 1)\)