Question

weeklyquiz - 12 6.1 - 6.3:
(1 point)
factor out the greatest common factor:
$9s^{2}t^{4}+6st - 21s=$
preview my answers submit answers
you have attempted this problem 0 times.
you have unlimited attempts remaining.

Explanation:

Step1: Find the GCF of coefficients

Find the GCF of \(9\), \(6\), and \(21\).
Factors of \(9\): \(1,3,9\)
Factors of \(6\): \(1,2,3,6\)
Factors of \(21\): \(1,3,7,21\)
GCF of coefficients is \(3\).

Step2: Find the GCF of variables

For variable \(s\):
Terms have \(s^{2}\), \(s\), \(s\). GCF of \(s^{2},s,s\) is \(s\).
For variable \(t\):
Terms have \(t^{4}\), \(t\), no \(t\) (in the third term). So GCF for \(t\) - related part is \(1\) (since the third term has no \(t\)).
So the GCF of the polynomial \(9s^{2}t^{4}+6st - 21s\) is \(3s\).

Step3: Factor out the GCF

Divide each term by \(3s\):
\(\frac{9s^{2}t^{4}}{3s}=3st^{4}\), \(\frac{6st}{3s} = 2t\), \(\frac{-21s}{3s}=-7\)

So \(9s^{2}t^{4}+6st - 21s=3s(3st^{4}+2t - 7)\)

Answer:

\(3s(3st^{4}+2t - 7)\)