Question

question
factor completely.
$9x^5z^7 - 33x^4y^4z^4$
answer attempt 1 out of 2

Explanation:

Step1: Find GCF of coefficients

The coefficients are 9 and 33. GCF of 9 and 33 is 3 (since \(9 = 3\times3\), \(33 = 3\times11\)).

Step2: Find GCF of variables

For \(x\): lowest power is \(x^4\) (in \(x^5\) and \(x^4\)).
For \(y\): only in second term, so no \(y\) in GCF.
For \(z\): lowest power is \(z^4\) (in \(z^7\) and \(z^4\)).
So GCF of variables is \(x^4z^4\).

Step3: Factor out GCF

Factor out \(3x^4z^4\) from \(9x^5z^7 - 33x^4y^4z^4\):
\(3x^4z^4(3xz^3 - 11y^4)\) (since \(9x^5z^7\div3x^4z^4 = 3xz^3\) and \(-33x^4y^4z^4\div3x^4z^4 = -11y^4\)).

Answer:

\(3x^4z^4(3xz^3 - 11y^4)\)