Question

factor out the greatest common monomial factor from the polynomial. (if the polynomial has no common monomial factor, enter ncf.)
$21x^{2}z^{5} + 35x^{6}z$

Explanation:

Step1: Find GCF of coefficients

Find GCF of 21 and 35. Factors of 21: 1, 3, 7, 21. Factors of 35: 1, 5, 7, 35. GCF is 7.

Step2: Find GCF of \(x\)-terms

For \(x^2\) and \(x^6\), the lowest power is \(x^2\).

Step3: Find GCF of \(z\)-terms

For \(z^5\) and \(z\), the lowest power is \(z\).

Step4: Factor out GCF

Factor out \(7x^2z\) from \(21x^2z^5 + 35x^6z\):
\(7x^2z(3z^4 + 5x^4)\)

Answer:

\(7x^2z(3z^4 + 5x^4)\)