QuestionFactor completely. $-19 x^{5}-4 x y z^{3}$

Studdy Solution

STEP 1

1. We are given the expression $-19x^5 - 4xyz^3$ .
2. The task is to factor the expression completely.
3. We will look for common factors and apply factoring techniques.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the terms.
2. Check if further factoring is possible for any remaining expressions.

STEP 3

Identify the greatest common factor (GCF) of the terms $-19x^5$ and $-4xyz^3$ .
The only common factor is $x$ , since both terms contain the variable $x$ .
Factor out the GCF, $x$ , from the expression:
$-19x^5 - 4xyz^3 = x(-19x^4 - 4yz^3)$

STEP 4

Check if the expression inside the parentheses, $-19x^4 - 4yz^3$ , can be factored further.
Since $-19$ and $-4$ have no common factors and the variables $x$ , $y$ , and $z$ do not share any further common factors, the expression inside the parentheses is already in its simplest form.
The completely factored form of the expression is:
$\boxed{x(-19x^4 - 4yz^3)}$

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